Sternschaltung \u2013 Formeln<\/title>\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=DM+Sans:wght@300;400;500;600;700&family=DM+Mono:wght@400;500&display=swap\" rel=\"stylesheet\">\n<style>\n :root {\n --pink-dark: #c0206e;\n --pink-light: #e91e8c;\n --magenta: #cc00aa;\n --text: #111;\n --text-light: #555;\n --border: #eee;\n }\n\n * { margin: 0; padding: 0; box-sizing: border-box; }\n\n body {\n font-family: 'DM Sans', sans-serif;\n background: #fff;\n color: var(--text);\n min-height: 100vh;\n padding: clamp(1rem, 4vw, 2rem) clamp(0.9rem, 4vw, 1.5rem) 4rem;\n }\n\n .content {\n max-width: 720px;\n margin: 0 auto;\n width: 100%;\n }\n\n \/* SECTION DIVIDER *\/\n .section-divider {\n display: flex;\n align-items: center;\n gap: 0.8rem;\n margin: 2rem 0 1rem;\n }\n .section-divider span {\n font-size: clamp(0.7rem, 2vw, 0.78rem);\n font-weight: 700;\n letter-spacing: 0.12em;\n text-transform: uppercase;\n color: #aaa;\n white-space: nowrap;\n }\n .section-divider::before,\n .section-divider::after {\n content: '';\n flex: 1;\n height: 1px;\n background: var(--border);\n }\n\n \/* STEP *\/\n .step {\n margin-bottom: clamp(0.8rem, 2vw, 1.2rem);\n border: 1px solid var(--border);\n border-radius: clamp(10px, 2vw, 16px);\n overflow: hidden;\n background: #fafafa;\n transition: box-shadow 0.2s;\n }\n .step:hover { box-shadow: 0 4px 20px rgba(200,0,100,0.07); }\n\n .step-header {\n display: flex;\n align-items: center;\n gap: 0.75rem;\n padding: clamp(0.7rem, 2vw, 1rem) clamp(0.9rem, 3vw, 1.3rem);\n border-bottom: 1px solid var(--border);\n background: #fff;\n flex-wrap: wrap;\n }\n .step-num {\n width: clamp(26px, 5vw, 32px);\n height: clamp(26px, 5vw, 32px);\n border-radius: 50%;\n background: linear-gradient(135deg, var(--pink-dark), var(--pink-light));\n color: #fff;\n font-weight: 700;\n font-size: clamp(0.75rem, 2vw, 0.85rem);\n display: flex; align-items: center; justify-content: center;\n flex-shrink: 0;\n }\n .step-title {\n font-size: clamp(0.85rem, 2.5vw, 0.95rem);\n font-weight: 600;\n flex: 1;\n min-width: 0;\n }\n .ks-badge {\n display: inline-block;\n background: linear-gradient(90deg, var(--pink-dark), var(--pink-light));\n color: #fff;\n font-size: clamp(0.55rem, 1.5vw, 0.65rem);\n font-weight: 600;\n letter-spacing: 0.09em;\n text-transform: uppercase;\n padding: 0.2rem 0.6rem;\n border-radius: 5px;\n margin-left: 0.4rem;\n white-space: nowrap;\n }\n\n .step-body {\n padding: clamp(0.9rem, 2.5vw, 1.2rem) clamp(0.9rem, 3vw, 1.3rem);\n }\n\n \/* FORMULA GRID *\/\n .formula-grid {\n display: grid;\n grid-template-columns: repeat(3, 1fr);\n gap: clamp(0.5rem, 2vw, 0.8rem);\n margin-top: 0.5rem;\n }\n .formula-grid-2 {\n display: grid;\n grid-template-columns: repeat(2, 1fr);\n gap: clamp(0.5rem, 2vw, 0.8rem);\n margin-top: 0.5rem;\n }\n .formula-card {\n background: #fff;\n border: 1px solid #e8e8e8;\n border-radius: clamp(8px, 2vw, 12px);\n padding: clamp(0.6rem, 2vw, 0.9rem) clamp(0.4rem, 2vw, 1rem);\n text-align: center;\n }\n .formula-label {\n font-size: clamp(0.55rem, 1.5vw, 0.65rem);\n font-weight: 600;\n letter-spacing: 0.08em;\n text-transform: uppercase;\n color: var(--text-light);\n margin-bottom: 0.45rem;\n }\n .formula-eq {\n font-family: 'DM Mono', monospace;\n font-size: clamp(0.78rem, 2.2vw, 1rem);\n font-weight: 500;\n line-height: 1.8;\n }\n .frac {\n display: inline-flex;\n flex-direction: column;\n align-items: center;\n vertical-align: middle;\n margin: 0 0.1rem;\n line-height: 1.15;\n }\n .frac .num { border-bottom: 1.5px solid var(--text); padding-bottom: 1px; }\n .frac .den { padding-top: 1px; }\n .sub { font-size: 0.65em; vertical-align: sub; color: var(--magenta); font-weight: 600; }\n .sup { font-size: 0.65em; vertical-align: super; color: var(--pink-dark); font-weight: 600; }\n\n \/* FULL WIDTH FORMULA *\/\n .formula-full {\n background: #fff;\n border: 1px solid #e8e8e8;\n border-radius: clamp(8px, 2vw, 12px);\n padding: clamp(0.7rem, 2vw, 1rem) clamp(0.9rem, 2vw, 1.2rem);\n margin-top: 0.6rem;\n font-family: 'DM Mono', monospace;\n font-size: clamp(0.82rem, 2.2vw, 0.95rem);\n font-weight: 500;\n line-height: 1.8;\n }\n .formula-full .label {\n font-family: 'DM Sans', sans-serif;\n font-size: clamp(0.58rem, 1.5vw, 0.65rem);\n font-weight: 600;\n letter-spacing: 0.08em;\n text-transform: uppercase;\n color: var(--text-light);\n margin-bottom: 0.4rem;\n }\n\n \/* PILL *\/\n .formula-pill {\n display: inline-block;\n font-family: 'DM Mono', monospace;\n font-size: clamp(0.82rem, 2.5vw, 0.95rem);\n background: #fff;\n border: 1px solid #e0e0e0;\n border-radius: 8px;\n padding: 0.5rem clamp(0.7rem, 2vw, 1.1rem);\n margin-top: 0.2rem;\n }\n\n \/* HINT *\/\n .hint {\n margin-top: 0.8rem;\n padding: 0.7rem 1rem;\n background: #fff5fa;\n border-left: 3px solid var(--pink-light);\n border-radius: 0 8px 8px 0;\n font-size: clamp(0.78rem, 2vw, 0.85rem);\n color: var(--text-light);\n line-height: 1.5;\n }\n .hint strong { color: var(--pink-dark); }\n\n \/* INFO BOX *\/\n .info-box {\n margin-top: 0.8rem;\n padding: 0.7rem 1rem;\n background: #f5f5ff;\n border-left: 3px solid #7788ee;\n border-radius: 0 8px 8px 0;\n font-size: clamp(0.78rem, 2vw, 0.85rem);\n color: var(--text-light);\n line-height: 1.5;\n }\n .info-box strong { color: #3355cc; }\n\n \/* ANGLES *\/\n .angle-table { display: flex; flex-wrap: wrap; gap: 0.5rem; margin: 0.6rem 0 0.9rem; }\n .angle-chip {\n font-family: 'DM Mono', monospace;\n font-size: clamp(0.72rem, 2vw, 0.8rem);\n padding: 0.3rem 0.75rem;\n border-radius: 6px;\n font-weight: 500;\n }\n .angle-chip.pos { background: #fff0f5; color: var(--pink-dark); border: 1px solid #f9c0d8; }\n .angle-chip.neg { background: #f0f5ff; color: #3355cc; border: 1px solid #c0cef9; }\n\n \/* TEILSPANNUNG *\/\n .teilsp-grid {\n display: grid;\n grid-template-columns: 1fr 1fr;\n gap: clamp(0.5rem, 2vw, 0.8rem);\n margin-top: 0.6rem;\n }\n .teilsp-card {\n background: #fff;\n border: 1px solid #e8e8e8;\n border-radius: clamp(8px, 2vw, 12px);\n padding: clamp(0.7rem, 2vw, 0.85rem) 1rem;\n text-align: center;\n }\n .teilsp-card .label {\n font-size: clamp(0.58rem, 1.5vw, 0.65rem);\n font-weight: 600;\n text-transform: uppercase;\n letter-spacing: 0.08em;\n color: var(--text-light);\n margin-bottom: 0.35rem;\n }\n .teilsp-card .eq {\n font-family: 'DM Mono', monospace;\n font-size: clamp(0.82rem, 2.5vw, 0.9rem);\n font-weight: 500;\n }\n .pink { color: var(--magenta); }\n .blue { color: #3355cc; }\n\n .desc {\n font-size: clamp(0.78rem, 2vw, 0.83rem);\n color: var(--text-light);\n margin-bottom: 0.8rem;\n }\n .section-sub-label {\n font-size: clamp(0.58rem, 1.5vw, 0.7rem);\n font-weight: 600;\n text-transform: uppercase;\n letter-spacing: 0.08em;\n color: var(--text-light);\n margin-bottom: 0.45rem;\n }\n\n \/* RESPONSIVE *\/\n @media (max-width: 640px) {\n .formula-grid { grid-template-columns: 1fr 1fr; }\n }\n @media (max-width: 400px) {\n .formula-grid { grid-template-columns: 1fr; }\n .formula-grid-2 { grid-template-columns: 1fr; }\n .teilsp-grid { grid-template-columns: 1fr; }\n }\n<\/style>\n<\/head>\n<body>\n<div class=\"content\">\n\n \n\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">1<\/div>\n <div class=\"step-title\">Z<sub>1<\/sub>, Z<sub>2<\/sub>, Z<sub>3<\/sub> bestimmen <span class=\"ks-badge\">Exponential<\/span><\/div>\n <\/div>\n <div class=\"step-body\">\n <p class=\"desc\">Impedanzen jedes Strangs im Exponentialformat bestimmen:<\/p>\n <div class=\"formula-grid\">\n <div class=\"formula-card\">\n <div class=\"formula-label\">Strang 1<\/div>\n <div class=\"formula-eq\">Z<span class=\"sub\">1<\/span> = |Z<span class=\"sub\">1<\/span>| \u00b7 e<span class=\"sup\">j\u03c6\u2081<\/span><\/div>\n <\/div>\n <div class=\"formula-card\">\n <div class=\"formula-label\">Strang 2<\/div>\n <div class=\"formula-eq\">Z<span class=\"sub\">2<\/span> = |Z<span class=\"sub\">2<\/span>| \u00b7 e<span class=\"sup\">j\u03c6\u2082<\/span><\/div>\n <\/div>\n <div class=\"formula-card\">\n <div class=\"formula-label\">Strang 3<\/div>\n <div class=\"formula-eq\">Z<span class=\"sub\">3<\/span> = |Z<span class=\"sub\">3<\/span>| \u00b7 e<span class=\"sup\">j\u03c6\u2083<\/span><\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">2<\/div>\n <div class=\"step-title\">Strom im Neutralleiter berechnen<\/div>\n <\/div>\n <div class=\"step-body\">\n\n <div class=\"formula-full\">\n I<span class=\"sub\">N<\/span> =\n <span class=\"frac\" style=\"font-size:1.05em; vertical-align:middle;\">\n <span class=\"num\" style=\"padding: 2px 6px 4px;\">\n <span class=\"frac\">\n <span class=\"num\">U<span class=\"sub\">R<\/span><\/span>\n <span class=\"den\">Z<span class=\"sub\">1<\/span><\/span>\n <\/span>\n + \n <span class=\"frac\">\n <span class=\"num\">U<span class=\"sub\">S<\/span><\/span>\n <span class=\"den\">Z<span class=\"sub\">2<\/span><\/span>\n <\/span>\n + \n <span class=\"frac\">\n <span class=\"num\">U<span class=\"sub\">T<\/span><\/span>\n <span class=\"den\">Z<span class=\"sub\">3<\/span><\/span>\n <\/span>\n <\/span>\n <span class=\"den\" style=\"padding: 4px 6px 2px;\">\n 1 + Z<span class=\"sub\">N<\/span> \u00b7 (\n <span class=\"frac\">\n <span class=\"num\">1<\/span>\n <span class=\"den\">Z<span class=\"sub\">1<\/span><\/span>\n <\/span>\n + \n <span class=\"frac\">\n <span class=\"num\">1<\/span>\n <span class=\"den\">Z<span class=\"sub\">2<\/span><\/span>\n <\/span>\n + \n <span class=\"frac\">\n <span class=\"num\">1<\/span>\n <span class=\"den\">Z<span class=\"sub\">3<\/span><\/span>\n <\/span>\n )\n <\/span>\n <\/span>\n <\/div>\n <\/div>\n <\/div>\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">3<\/div>\n <div class=\"step-title\">Spannung im Neutralleiter berechnen<\/div>\n <\/div>\n <div class=\"step-body\">\n <div class=\"formula-pill\">\n U<span class=\"sub\">N’N<\/span> = I<span class=\"sub\">N<\/span> \u00b7 Z<span class=\"sub\">N<\/span>\n <\/div>\n <div class=\"hint\">\n <strong>Z<sub>N<\/sub> = X<sub>R<\/sub>:<\/strong> Die Neutralleiterimpedanz ist rein reaktiv (induktiv) \u2014 Winkel +90\u00b0\n <\/div>\n <\/div>\n <\/div>\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">4<\/div>\n <div class=\"step-title\">Strangstrom berechnen<\/div>\n <\/div>\n <div class=\"step-body\">\n <p class=\"desc\">Mit der verschobenen Sternpunktspannung U<sub>N’N<\/sub> werden die tats\u00e4chlichen Strangspannungen und -str\u00f6me berechnet:<\/p>\n <div class=\"formula-grid\">\n <div class=\"formula-card\">\n <div class=\"formula-label\">Strang R<\/div>\n <div class=\"formula-eq\">\n I<span class=\"sub\">1<\/span> =\n <span class=\"frac\">\n <span class=\"num\">U<span class=\"sub\">R<\/span> \u2212 U<span class=\"sub\">N’N<\/span><\/span>\n <span class=\"den\">Z<span class=\"sub\">1<\/span><\/span>\n <\/span>\n <\/div>\n <\/div>\n <div class=\"formula-card\">\n <div class=\"formula-label\">Strang S<\/div>\n <div class=\"formula-eq\">\n I<span class=\"sub\">2<\/span> =\n <span class=\"frac\">\n <span class=\"num\">U<span class=\"sub\">S<\/span> \u2212 U<span class=\"sub\">N’N<\/span><\/span>\n <span class=\"den\">Z<span class=\"sub\">2<\/span><\/span>\n <\/span>\n <\/div>\n <\/div>\n <div class=\"formula-card\">\n <div class=\"formula-label\">Strang T<\/div>\n <div class=\"formula-eq\">\n I<span class=\"sub\">3<\/span> =\n <span class=\"frac\">\n <span class=\"num\">U<span class=\"sub\">T<\/span> \u2212 U<span class=\"sub\">N’N<\/span><\/span>\n <span class=\"den\">Z<span class=\"sub\">3<\/span><\/span>\n <\/span>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">5<\/div>\n <div class=\"step-title\">Spannung am Verbraucher berechnen<\/div>\n <\/div>\n <div class=\"step-body\">\n <p class=\"desc\">Tats\u00e4chliche Verbraucherspannung je Strang (Strangspannung minus Sternpunktverschiebung):<\/p>\n <div class=\"formula-grid\">\n <div class=\"formula-card\">\n <div class=\"formula-label\">Verbraucher 1<\/div>\n <div class=\"formula-eq\">U<span class=\"sub\">1<\/span> = Z<span class=\"sub\">1<\/span> \u00b7 I<span class=\"sub\">1<\/span><\/div>\n <\/div>\n <div class=\"formula-card\">\n <div class=\"formula-label\">Verbraucher 2<\/div>\n <div class=\"formula-eq\">U<span class=\"sub\">2<\/span> = Z<span class=\"sub\">2<\/span> \u00b7 I<span class=\"sub\">2<\/span><\/div>\n <\/div>\n <div class=\"formula-card\">\n <div class=\"formula-label\">Verbraucher 3<\/div>\n <div class=\"formula-eq\">U<span class=\"sub\">3<\/span> = Z<span class=\"sub\">3<\/span> \u00b7 I<span class=\"sub\">3<\/span><\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">6<\/div>\n <div class=\"step-title\">Teilspannungen bei kombinierten Bauteilen berechnen <span class=\"ks-badge\">R + X<sub>L<\/sub> \/ R \u2212 X<sub>C<\/sub><\/span><\/div>\n <\/div>\n <div class=\"step-body\">\n <p class=\"desc\">G\u00fcltig f\u00fcr Kombinationen: <strong>R + X<sub>L<\/sub><\/strong> \/ <strong>R \u2212 X<sub>C<\/sub><\/strong><\/p>\n <div class=\"section-sub-label\">Phasenwinkel<\/div>\n <div class=\"angle-table\">\n <div class=\"angle-chip pos\">X<sub>L<\/sub> \u2192 +90\u00b0<\/div>\n <div class=\"angle-chip neg\">X<sub>C<\/sub> \u2192 \u221290\u00b0<\/div>\n <\/div>\n <div class=\"teilsp-grid\">\n <div class=\"teilsp-card\">\n <div class=\"label\">Widerstand<\/div>\n <div class=\"eq\">U<sub style=\"font-size:0.65em;\">R1<\/sub> = R<sub style=\"font-size:0.65em;\">1<\/sub> \u00b7 I<sub style=\"font-size:0.65em;\">1<\/sub><\/div>\n <\/div>\n <div class=\"teilsp-card\">\n <div class=\"label\">Induktivit\u00e4t<\/div>\n <div class=\"eq pink\">U<sub style=\"font-size:0.65em;\">XL<\/sub> = X<sub style=\"font-size:0.65em;\">L<\/sub> \u00b7 I<sub style=\"font-size:0.65em;\">1<\/sub><\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n\n\n \n <div class=\"section-divider\"><span>Leistungsberechnung<\/span><\/div>\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">7<\/div>\n <div class=\"step-title\">Scheinleistung S<sub>1<\/sub> berechnen <span class=\"ks-badge\">Exponential<\/span><\/div>\n <\/div>\n <div class=\"step-body\">\n <p class=\"desc\">U<sub>Str<\/sub> mal konjugiert komplexen Strom (Vorzeichen des Winkels tauschen) \u2014 je nach Sternschaltung: U<sub>R<\/sub>, U<sub>S<\/sub>, U<sub>T<\/sub><\/p>\n <div class=\"formula-full\">\n <div class=\"label\">Scheinleistung Strang 1<\/div>\n S<span class=\"sub\">1<\/span> = U<span class=\"sub\">Str<\/span> \u00b7 I<span class=\"sub\">1<\/span><span class=\"sup\">*<\/span> \u2192 <span style=\"color:var(--pink-dark);\">Exponentialform<\/span>\n <\/div>\n <div class=\"hint\">\n <strong>Konjugiert:<\/strong> Vorzeichen des Winkels von I<sub>1<\/sub> wechseln \u2192 I<sub>1<\/sub><sup>*<\/sup>\n <\/div>\n <\/div>\n <\/div>\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">8<\/div>\n <div class=\"step-title\">Exponential \u2192 Arithmetisch umrechnen<\/div>\n <\/div>\n <div class=\"step-body\">\n <p class=\"desc\">S in arithmetische Form umrechnen, um Real- und Imagin\u00e4rteil abzulesen:<\/p>\n <div class=\"formula-grid-2\">\n <div class=\"formula-card\">\n <div class=\"formula-label\">Wirkleistung P [W]<\/div>\n <div class=\"formula-eq\">P = Re(S<span class=\"sub\">1<\/span>)<\/div>\n <\/div>\n <div class=\"formula-card\">\n <div class=\"formula-label\">Blindleistung Q [Var]<\/div>\n <div class=\"formula-eq\">Q = Im(S<span class=\"sub\">1<\/span>)<\/div>\n <\/div>\n <\/div>\n <div class=\"hint\">\n <strong>Wiederholen<\/strong> f\u00fcr S<sub>2<\/sub> und S<sub>3<\/sub> (gleiche Vorgehensweise)\n <\/div>\n <\/div>\n <\/div>\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">9<\/div>\n <div class=\"step-title\">Gesamtleistung S<sub>ges<\/sub> berechnen<\/div>\n <\/div>\n <div class=\"step-body\">\n <div class=\"formula-pill\">\n S<span class=\"sub\">ges<\/span> [VA] = S<span class=\"sub\">1<\/span> + S<span class=\"sub\">2<\/span> + S<span class=\"sub\">3<\/span>\n <\/div>\n <div class=\"formula-grid-2\" style=\"margin-top:0.8rem;\">\n <div class=\"formula-card\">\n <div class=\"formula-label\">Gesamte Wirkleistung<\/div>\n <div class=\"formula-eq\">P<span class=\"sub\">ges<\/span> = Re(S<span class=\"sub\">ges<\/span>)<\/div>\n <\/div>\n <div class=\"formula-card\">\n <div class=\"formula-label\">Gesamte Blindleistung<\/div>\n <div class=\"formula-eq\">Q<span class=\"sub\">ges<\/span> = Im(S<span class=\"sub\">ges<\/span>)<\/div>\n <\/div>\n <\/div>\n <div class=\"hint\">\n <strong>Exp \u2192 Arith:<\/strong> P<sub>ges<\/sub> und Q<sub>ges<\/sub> aus S<sub>ges<\/sub> ablesen \u00b7 P<sub>ges<\/sub> = P<sub>ab<\/sub>\n <\/div>\n <\/div>\n <\/div>\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">10<\/div>\n <div class=\"step-title\">Scheinleistung effektiv berechnen <span class=\"ks-badge\">ohne Winkel<\/span><\/div>\n <\/div>\n <div class=\"step-body\">\n <p class=\"desc\">F\u00fcr die Scheinleistung ohne Winkelberechnung (Effektivwerte):<\/p>\n\n <div class=\"formula-full\" style=\"margin-top:0;\">\n <div class=\"label\">Effektivspannung<\/div>\n U<span class=\"sub\">effektiv<\/span> = 400 V\n <\/div>\n\n <div class=\"formula-full\">\n <div class=\"label\">Effektivstrom<\/div>\n <span style=\"display:inline-flex; align-items:center; gap:0; vertical-align:middle;\">\n I<span class=\"sub\">effektiv<\/span> = \n <span style=\"display:inline-flex; align-items:stretch;\">\n <span style=\"font-size:2em; line-height:1; font-weight:300; transform:scaleY(0.85); display:inline-block;\">\u221a<\/span>\n <span style=\"display:inline-flex; flex-direction:column; border-top:1.5px solid var(--text); padding:2px 6px 0; justify-content:center;\">\n <span class=\"frac\">\n <span class=\"num\" style=\"border-bottom:none; white-space:nowrap;\">|I<span class=\"sub\">1<\/span>|<span class=\"sup\">2<\/span> + |I<span class=\"sub\">2<\/span>|<span class=\"sup\">2<\/span> + |I<span class=\"sub\">3<\/span>|<span class=\"sup\">2<\/span><\/span>\n <span class=\"den\" style=\"text-align:center;\">3<\/span>\n <\/span>\n <\/span>\n <\/span>\n <\/span>\n <\/div>\n\n <div class=\"formula-full\">\n <div class=\"label\">Scheinleistung effektiv<\/div>\n S<span class=\"sub\">effektiv<\/span> = U<span class=\"sub\">effektiv<\/span> \u00b7 I<span class=\"sub\">effektiv<\/span>\n <\/div>\n <\/div>\n <\/div>\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">11<\/div>\n <div class=\"step-title\">Wirkungsgrad \u03b7 & Leistungsfaktor cos \u03c6<\/div>\n <\/div>\n <div class=\"step-body\">\n <div class=\"formula-grid-2\">\n <div class=\"formula-card\">\n <div class=\"formula-label\">Wirkungsgrad \u03b7 [%]<\/div>\n <div class=\"formula-eq\">\n \u03b7 =\n <span class=\"frac\">\n <span class=\"num\">P<span class=\"sub\">ab<\/span><\/span>\n <span class=\"den\">P<span class=\"sub\">zu<\/span><\/span>\n <\/span>\n =\n <span class=\"frac\">\n <span class=\"num\">P<span class=\"sub\">ges<\/span><\/span>\n <span class=\"den\">S<span class=\"sub\">effektiv<\/span><\/span>\n <\/span>\n <\/div>\n <\/div>\n <div class=\"formula-card\">\n <div class=\"formula-label\">Leistungsfaktor<\/div>\n <div class=\"formula-eq\">cos \u03c6 = cos(\u2220S<span class=\"sub\">ges<\/span>)<\/div>\n <\/div>\n <\/div>\n <div class=\"info-box\">\n <strong>Hinweis:<\/strong> \u03b7 in % angeben \u00b7 cos \u03c6 ist der Winkel von S<sub>ges<\/sub> im Exponentialformat\n <\/div>\n <\/div>\n <\/div>\n\n<\/div>\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>Sternschaltung \u2013 Formeln 1 Z1, Z2, Z3 bestimmen Exponential Impedanzen jedes Strangs im Exponentialformat bestimmen: Strang 1 Z1 = |Z1| \u00b7 ej\u03c6\u2081 Strang 2 Z2 = |Z2| \u00b7 ej\u03c6\u2082 Strang 3 Z3 = |Z3| \u00b7 ej\u03c6\u2083 2 Strom im Neutralleiter berechnen IN = UR Z1 + US Z2 + UT […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_themeisle_gutenberg_block_has_review":false,"footnotes":""},"class_list":["post-150","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/fseschueler19.bplaced.net\/wordpress\/wp-json\/wp\/v2\/pages\/150","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fseschueler19.bplaced.net\/wordpress\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/fseschueler19.bplaced.net\/wordpress\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/fseschueler19.bplaced.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fseschueler19.bplaced.net\/wordpress\/wp-json\/wp\/v2\/comments?post=150"}],"version-history":[{"count":4,"href":"https:\/\/fseschueler19.bplaced.net\/wordpress\/wp-json\/wp\/v2\/pages\/150\/revisions"}],"predecessor-version":[{"id":200,"href":"https:\/\/fseschueler19.bplaced.net\/wordpress\/wp-json\/wp\/v2\/pages\/150\/revisions\/200"}],"wp:attachment":[{"href":"https:\/\/fseschueler19.bplaced.net\/wordpress\/wp-json\/wp\/v2\/media?parent=150"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

<\/div>\n\n\n\n\n\n\n\n\nSternschaltung \u2013 Formeln<\/title>\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=DM+Sans:wght@300;400;500;600;700&family=DM+Mono:wght@400;500&display=swap\" rel=\"stylesheet\">\n<style>\n :root {\n --pink-dark: #c0206e;\n --pink-light: #e91e8c;\n --magenta: #cc00aa;\n --text: #111;\n --text-light: #555;\n --border: #eee;\n }\n\n * { margin: 0; padding: 0; box-sizing: border-box; }\n\n body {\n font-family: 'DM Sans', sans-serif;\n background: #fff;\n color: var(--text);\n min-height: 100vh;\n padding: clamp(1rem, 4vw, 2rem) clamp(0.9rem, 4vw, 1.5rem) 4rem;\n }\n\n .content {\n max-width: 720px;\n margin: 0 auto;\n width: 100%;\n }\n\n \/* SECTION DIVIDER *\/\n .section-divider {\n display: flex;\n align-items: center;\n gap: 0.8rem;\n margin: 2rem 0 1rem;\n }\n .section-divider span {\n font-size: clamp(0.7rem, 2vw, 0.78rem);\n font-weight: 700;\n letter-spacing: 0.12em;\n text-transform: uppercase;\n color: #aaa;\n white-space: nowrap;\n }\n .section-divider::before,\n .section-divider::after {\n content: '';\n flex: 1;\n height: 1px;\n background: var(--border);\n }\n\n \/* STEP *\/\n .step {\n margin-bottom: clamp(0.8rem, 2vw, 1.2rem);\n border: 1px solid var(--border);\n border-radius: clamp(10px, 2vw, 16px);\n overflow: hidden;\n background: #fafafa;\n transition: box-shadow 0.2s;\n }\n .step:hover { box-shadow: 0 4px 20px rgba(200,0,100,0.07); }\n\n .step-header {\n display: flex;\n align-items: center;\n gap: 0.75rem;\n padding: clamp(0.7rem, 2vw, 1rem) clamp(0.9rem, 3vw, 1.3rem);\n border-bottom: 1px solid var(--border);\n background: #fff;\n flex-wrap: wrap;\n }\n .step-num {\n width: clamp(26px, 5vw, 32px);\n height: clamp(26px, 5vw, 32px);\n border-radius: 50%;\n background: linear-gradient(135deg, var(--pink-dark), var(--pink-light));\n color: #fff;\n font-weight: 700;\n font-size: clamp(0.75rem, 2vw, 0.85rem);\n display: flex; align-items: center; justify-content: center;\n flex-shrink: 0;\n }\n .step-title {\n font-size: clamp(0.85rem, 2.5vw, 0.95rem);\n font-weight: 600;\n flex: 1;\n min-width: 0;\n }\n .ks-badge {\n display: inline-block;\n background: linear-gradient(90deg, var(--pink-dark), var(--pink-light));\n color: #fff;\n font-size: clamp(0.55rem, 1.5vw, 0.65rem);\n font-weight: 600;\n letter-spacing: 0.09em;\n text-transform: uppercase;\n padding: 0.2rem 0.6rem;\n border-radius: 5px;\n margin-left: 0.4rem;\n white-space: nowrap;\n }\n\n .step-body {\n padding: clamp(0.9rem, 2.5vw, 1.2rem) clamp(0.9rem, 3vw, 1.3rem);\n }\n\n \/* FORMULA GRID *\/\n .formula-grid {\n display: grid;\n grid-template-columns: repeat(3, 1fr);\n gap: clamp(0.5rem, 2vw, 0.8rem);\n margin-top: 0.5rem;\n }\n .formula-grid-2 {\n display: grid;\n grid-template-columns: repeat(2, 1fr);\n gap: clamp(0.5rem, 2vw, 0.8rem);\n margin-top: 0.5rem;\n }\n .formula-card {\n background: #fff;\n border: 1px solid #e8e8e8;\n border-radius: clamp(8px, 2vw, 12px);\n padding: clamp(0.6rem, 2vw, 0.9rem) clamp(0.4rem, 2vw, 1rem);\n text-align: center;\n }\n .formula-label {\n font-size: clamp(0.55rem, 1.5vw, 0.65rem);\n font-weight: 600;\n letter-spacing: 0.08em;\n text-transform: uppercase;\n color: var(--text-light);\n margin-bottom: 0.45rem;\n }\n .formula-eq {\n font-family: 'DM Mono', monospace;\n font-size: clamp(0.78rem, 2.2vw, 1rem);\n font-weight: 500;\n line-height: 1.8;\n }\n .frac {\n display: inline-flex;\n flex-direction: column;\n align-items: center;\n vertical-align: middle;\n margin: 0 0.1rem;\n line-height: 1.15;\n }\n .frac .num { border-bottom: 1.5px solid var(--text); padding-bottom: 1px; }\n .frac .den { padding-top: 1px; }\n .sub { font-size: 0.65em; vertical-align: sub; color: var(--magenta); font-weight: 600; }\n .sup { font-size: 0.65em; vertical-align: super; color: var(--pink-dark); font-weight: 600; }\n\n \/* FULL WIDTH FORMULA *\/\n .formula-full {\n background: #fff;\n border: 1px solid #e8e8e8;\n border-radius: clamp(8px, 2vw, 12px);\n padding: clamp(0.7rem, 2vw, 1rem) clamp(0.9rem, 2vw, 1.2rem);\n margin-top: 0.6rem;\n font-family: 'DM Mono', monospace;\n font-size: clamp(0.82rem, 2.2vw, 0.95rem);\n font-weight: 500;\n line-height: 1.8;\n }\n .formula-full .label {\n font-family: 'DM Sans', sans-serif;\n font-size: clamp(0.58rem, 1.5vw, 0.65rem);\n font-weight: 600;\n letter-spacing: 0.08em;\n text-transform: uppercase;\n color: var(--text-light);\n margin-bottom: 0.4rem;\n }\n\n \/* PILL *\/\n .formula-pill {\n display: inline-block;\n font-family: 'DM Mono', monospace;\n font-size: clamp(0.82rem, 2.5vw, 0.95rem);\n background: #fff;\n border: 1px solid #e0e0e0;\n border-radius: 8px;\n padding: 0.5rem clamp(0.7rem, 2vw, 1.1rem);\n margin-top: 0.2rem;\n }\n\n \/* HINT *\/\n .hint {\n margin-top: 0.8rem;\n padding: 0.7rem 1rem;\n background: #fff5fa;\n border-left: 3px solid var(--pink-light);\n border-radius: 0 8px 8px 0;\n font-size: clamp(0.78rem, 2vw, 0.85rem);\n color: var(--text-light);\n line-height: 1.5;\n }\n .hint strong { color: var(--pink-dark); }\n\n \/* INFO BOX *\/\n .info-box {\n margin-top: 0.8rem;\n padding: 0.7rem 1rem;\n background: #f5f5ff;\n border-left: 3px solid #7788ee;\n border-radius: 0 8px 8px 0;\n font-size: clamp(0.78rem, 2vw, 0.85rem);\n color: var(--text-light);\n line-height: 1.5;\n }\n .info-box strong { color: #3355cc; }\n\n \/* ANGLES *\/\n .angle-table { display: flex; flex-wrap: wrap; gap: 0.5rem; margin: 0.6rem 0 0.9rem; }\n .angle-chip {\n font-family: 'DM Mono', monospace;\n font-size: clamp(0.72rem, 2vw, 0.8rem);\n padding: 0.3rem 0.75rem;\n border-radius: 6px;\n font-weight: 500;\n }\n .angle-chip.pos { background: #fff0f5; color: var(--pink-dark); border: 1px solid #f9c0d8; }\n .angle-chip.neg { background: #f0f5ff; color: #3355cc; border: 1px solid #c0cef9; }\n\n \/* TEILSPANNUNG *\/\n .teilsp-grid {\n display: grid;\n grid-template-columns: 1fr 1fr;\n gap: clamp(0.5rem, 2vw, 0.8rem);\n margin-top: 0.6rem;\n }\n .teilsp-card {\n background: #fff;\n border: 1px solid #e8e8e8;\n border-radius: clamp(8px, 2vw, 12px);\n padding: clamp(0.7rem, 2vw, 0.85rem) 1rem;\n text-align: center;\n }\n .teilsp-card .label {\n font-size: clamp(0.58rem, 1.5vw, 0.65rem);\n font-weight: 600;\n text-transform: uppercase;\n letter-spacing: 0.08em;\n color: var(--text-light);\n margin-bottom: 0.35rem;\n }\n .teilsp-card .eq {\n font-family: 'DM Mono', monospace;\n font-size: clamp(0.82rem, 2.5vw, 0.9rem);\n font-weight: 500;\n }\n .pink { color: var(--magenta); }\n .blue { color: #3355cc; }\n\n .desc {\n font-size: clamp(0.78rem, 2vw, 0.83rem);\n color: var(--text-light);\n margin-bottom: 0.8rem;\n }\n .section-sub-label {\n font-size: clamp(0.58rem, 1.5vw, 0.7rem);\n font-weight: 600;\n text-transform: uppercase;\n letter-spacing: 0.08em;\n color: var(--text-light);\n margin-bottom: 0.45rem;\n }\n\n \/* RESPONSIVE *\/\n @media (max-width: 640px) {\n .formula-grid { grid-template-columns: 1fr 1fr; }\n }\n @media (max-width: 400px) {\n .formula-grid { grid-template-columns: 1fr; }\n .formula-grid-2 { grid-template-columns: 1fr; }\n .teilsp-grid { grid-template-columns: 1fr; }\n }\n<\/style>\n<\/head>\n<body>\n<div class=\"content\">\n\n \n\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">1<\/div>\n <div class=\"step-title\">Z<sub>1<\/sub>, Z<sub>2<\/sub>, Z<sub>3<\/sub> bestimmen <span class=\"ks-badge\">Exponential<\/span><\/div>\n <\/div>\n <div class=\"step-body\">\n <p class=\"desc\">Impedanzen jedes Strangs im Exponentialformat bestimmen:<\/p>\n <div class=\"formula-grid\">\n <div class=\"formula-card\">\n <div class=\"formula-label\">Strang 1<\/div>\n <div class=\"formula-eq\">Z<span class=\"sub\">1<\/span> = |Z<span class=\"sub\">1<\/span>| \u00b7 e<span class=\"sup\">j\u03c6\u2081<\/span><\/div>\n <\/div>\n <div class=\"formula-card\">\n <div class=\"formula-label\">Strang 2<\/div>\n <div class=\"formula-eq\">Z<span class=\"sub\">2<\/span> = |Z<span class=\"sub\">2<\/span>| \u00b7 e<span class=\"sup\">j\u03c6\u2082<\/span><\/div>\n <\/div>\n <div class=\"formula-card\">\n <div class=\"formula-label\">Strang 3<\/div>\n <div class=\"formula-eq\">Z<span class=\"sub\">3<\/span> = |Z<span class=\"sub\">3<\/span>| \u00b7 e<span class=\"sup\">j\u03c6\u2083<\/span><\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">2<\/div>\n <div class=\"step-title\">Strom im Neutralleiter berechnen<\/div>\n <\/div>\n <div class=\"step-body\">\n\n <div class=\"formula-full\">\n I<span class=\"sub\">N<\/span> =\n <span class=\"frac\" style=\"font-size:1.05em; vertical-align:middle;\">\n <span class=\"num\" style=\"padding: 2px 6px 4px;\">\n <span class=\"frac\">\n <span class=\"num\">U<span class=\"sub\">R<\/span><\/span>\n <span class=\"den\">Z<span class=\"sub\">1<\/span><\/span>\n <\/span>\n + \n <span class=\"frac\">\n <span class=\"num\">U<span class=\"sub\">S<\/span><\/span>\n <span class=\"den\">Z<span class=\"sub\">2<\/span><\/span>\n <\/span>\n + \n <span class=\"frac\">\n <span class=\"num\">U<span class=\"sub\">T<\/span><\/span>\n <span class=\"den\">Z<span class=\"sub\">3<\/span><\/span>\n <\/span>\n <\/span>\n <span class=\"den\" style=\"padding: 4px 6px 2px;\">\n 1 + Z<span class=\"sub\">N<\/span> \u00b7 (\n <span class=\"frac\">\n <span class=\"num\">1<\/span>\n <span class=\"den\">Z<span class=\"sub\">1<\/span><\/span>\n <\/span>\n + \n <span class=\"frac\">\n <span class=\"num\">1<\/span>\n <span class=\"den\">Z<span class=\"sub\">2<\/span><\/span>\n <\/span>\n + \n <span class=\"frac\">\n <span class=\"num\">1<\/span>\n <span class=\"den\">Z<span class=\"sub\">3<\/span><\/span>\n <\/span>\n )\n <\/span>\n <\/span>\n <\/div>\n <\/div>\n <\/div>\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">3<\/div>\n <div class=\"step-title\">Spannung im Neutralleiter berechnen<\/div>\n <\/div>\n <div class=\"step-body\">\n <div class=\"formula-pill\">\n U<span class=\"sub\">N’N<\/span> = I<span class=\"sub\">N<\/span> \u00b7 Z<span class=\"sub\">N<\/span>\n <\/div>\n <div class=\"hint\">\n <strong>Z<sub>N<\/sub> = X<sub>R<\/sub>:<\/strong> Die Neutralleiterimpedanz ist rein reaktiv (induktiv) \u2014 Winkel +90\u00b0\n <\/div>\n <\/div>\n <\/div>\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">4<\/div>\n <div class=\"step-title\">Strangstrom berechnen<\/div>\n <\/div>\n <div class=\"step-body\">\n <p class=\"desc\">Mit der verschobenen Sternpunktspannung U<sub>N’N<\/sub> werden die tats\u00e4chlichen Strangspannungen und -str\u00f6me berechnet:<\/p>\n <div class=\"formula-grid\">\n <div class=\"formula-card\">\n <div class=\"formula-label\">Strang R<\/div>\n <div class=\"formula-eq\">\n I<span class=\"sub\">1<\/span> =\n <span class=\"frac\">\n <span class=\"num\">U<span class=\"sub\">R<\/span> \u2212 U<span class=\"sub\">N’N<\/span><\/span>\n <span class=\"den\">Z<span class=\"sub\">1<\/span><\/span>\n <\/span>\n <\/div>\n <\/div>\n <div class=\"formula-card\">\n <div class=\"formula-label\">Strang S<\/div>\n <div class=\"formula-eq\">\n I<span class=\"sub\">2<\/span> =\n <span class=\"frac\">\n <span class=\"num\">U<span class=\"sub\">S<\/span> \u2212 U<span class=\"sub\">N’N<\/span><\/span>\n <span class=\"den\">Z<span class=\"sub\">2<\/span><\/span>\n <\/span>\n <\/div>\n <\/div>\n <div class=\"formula-card\">\n <div class=\"formula-label\">Strang T<\/div>\n <div class=\"formula-eq\">\n I<span class=\"sub\">3<\/span> =\n <span class=\"frac\">\n <span class=\"num\">U<span class=\"sub\">T<\/span> \u2212 U<span class=\"sub\">N’N<\/span><\/span>\n <span class=\"den\">Z<span class=\"sub\">3<\/span><\/span>\n <\/span>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">5<\/div>\n <div class=\"step-title\">Spannung am Verbraucher berechnen<\/div>\n <\/div>\n <div class=\"step-body\">\n <p class=\"desc\">Tats\u00e4chliche Verbraucherspannung je Strang (Strangspannung minus Sternpunktverschiebung):<\/p>\n <div class=\"formula-grid\">\n <div class=\"formula-card\">\n <div class=\"formula-label\">Verbraucher 1<\/div>\n <div class=\"formula-eq\">U<span class=\"sub\">1<\/span> = Z<span class=\"sub\">1<\/span> \u00b7 I<span class=\"sub\">1<\/span><\/div>\n <\/div>\n <div class=\"formula-card\">\n <div class=\"formula-label\">Verbraucher 2<\/div>\n <div class=\"formula-eq\">U<span class=\"sub\">2<\/span> = Z<span class=\"sub\">2<\/span> \u00b7 I<span class=\"sub\">2<\/span><\/div>\n <\/div>\n <div class=\"formula-card\">\n <div class=\"formula-label\">Verbraucher 3<\/div>\n <div class=\"formula-eq\">U<span class=\"sub\">3<\/span> = Z<span class=\"sub\">3<\/span> \u00b7 I<span class=\"sub\">3<\/span><\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">6<\/div>\n <div class=\"step-title\">Teilspannungen bei kombinierten Bauteilen berechnen <span class=\"ks-badge\">R + X<sub>L<\/sub> \/ R \u2212 X<sub>C<\/sub><\/span><\/div>\n <\/div>\n <div class=\"step-body\">\n <p class=\"desc\">G\u00fcltig f\u00fcr Kombinationen: <strong>R + X<sub>L<\/sub><\/strong> \/ <strong>R \u2212 X<sub>C<\/sub><\/strong><\/p>\n <div class=\"section-sub-label\">Phasenwinkel<\/div>\n <div class=\"angle-table\">\n <div class=\"angle-chip pos\">X<sub>L<\/sub> \u2192 +90\u00b0<\/div>\n <div class=\"angle-chip neg\">X<sub>C<\/sub> \u2192 \u221290\u00b0<\/div>\n <\/div>\n <div class=\"teilsp-grid\">\n <div class=\"teilsp-card\">\n <div class=\"label\">Widerstand<\/div>\n <div class=\"eq\">U<sub style=\"font-size:0.65em;\">R1<\/sub> = R<sub style=\"font-size:0.65em;\">1<\/sub> \u00b7 I<sub style=\"font-size:0.65em;\">1<\/sub><\/div>\n <\/div>\n <div class=\"teilsp-card\">\n <div class=\"label\">Induktivit\u00e4t<\/div>\n <div class=\"eq pink\">U<sub style=\"font-size:0.65em;\">XL<\/sub> = X<sub style=\"font-size:0.65em;\">L<\/sub> \u00b7 I<sub style=\"font-size:0.65em;\">1<\/sub><\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n\n\n \n <div class=\"section-divider\"><span>Leistungsberechnung<\/span><\/div>\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">7<\/div>\n <div class=\"step-title\">Scheinleistung S<sub>1<\/sub> berechnen <span class=\"ks-badge\">Exponential<\/span><\/div>\n <\/div>\n <div class=\"step-body\">\n <p class=\"desc\">U<sub>Str<\/sub> mal konjugiert komplexen Strom (Vorzeichen des Winkels tauschen) \u2014 je nach Sternschaltung: U<sub>R<\/sub>, U<sub>S<\/sub>, U<sub>T<\/sub><\/p>\n <div class=\"formula-full\">\n <div class=\"label\">Scheinleistung Strang 1<\/div>\n S<span class=\"sub\">1<\/span> = U<span class=\"sub\">Str<\/span> \u00b7 I<span class=\"sub\">1<\/span><span class=\"sup\">*<\/span> \u2192 <span style=\"color:var(--pink-dark);\">Exponentialform<\/span>\n <\/div>\n <div class=\"hint\">\n <strong>Konjugiert:<\/strong> Vorzeichen des Winkels von I<sub>1<\/sub> wechseln \u2192 I<sub>1<\/sub><sup>*<\/sup>\n <\/div>\n <\/div>\n <\/div>\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">8<\/div>\n <div class=\"step-title\">Exponential \u2192 Arithmetisch umrechnen<\/div>\n <\/div>\n <div class=\"step-body\">\n <p class=\"desc\">S in arithmetische Form umrechnen, um Real- und Imagin\u00e4rteil abzulesen:<\/p>\n <div class=\"formula-grid-2\">\n <div class=\"formula-card\">\n <div class=\"formula-label\">Wirkleistung P [W]<\/div>\n <div class=\"formula-eq\">P = Re(S<span class=\"sub\">1<\/span>)<\/div>\n <\/div>\n <div class=\"formula-card\">\n <div class=\"formula-label\">Blindleistung Q [Var]<\/div>\n <div class=\"formula-eq\">Q = Im(S<span class=\"sub\">1<\/span>)<\/div>\n <\/div>\n <\/div>\n <div class=\"hint\">\n <strong>Wiederholen<\/strong> f\u00fcr S<sub>2<\/sub> und S<sub>3<\/sub> (gleiche Vorgehensweise)\n <\/div>\n <\/div>\n <\/div>\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">9<\/div>\n <div class=\"step-title\">Gesamtleistung S<sub>ges<\/sub> berechnen<\/div>\n <\/div>\n <div class=\"step-body\">\n <div class=\"formula-pill\">\n S<span class=\"sub\">ges<\/span> [VA] = S<span class=\"sub\">1<\/span> + S<span class=\"sub\">2<\/span> + S<span class=\"sub\">3<\/span>\n <\/div>\n <div class=\"formula-grid-2\" style=\"margin-top:0.8rem;\">\n <div class=\"formula-card\">\n <div class=\"formula-label\">Gesamte Wirkleistung<\/div>\n <div class=\"formula-eq\">P<span class=\"sub\">ges<\/span> = Re(S<span class=\"sub\">ges<\/span>)<\/div>\n <\/div>\n <div class=\"formula-card\">\n <div class=\"formula-label\">Gesamte Blindleistung<\/div>\n <div class=\"formula-eq\">Q<span class=\"sub\">ges<\/span> = Im(S<span class=\"sub\">ges<\/span>)<\/div>\n <\/div>\n <\/div>\n <div class=\"hint\">\n <strong>Exp \u2192 Arith:<\/strong> P<sub>ges<\/sub> und Q<sub>ges<\/sub> aus S<sub>ges<\/sub> ablesen \u00b7 P<sub>ges<\/sub> = P<sub>ab<\/sub>\n <\/div>\n <\/div>\n <\/div>\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">10<\/div>\n <div class=\"step-title\">Scheinleistung effektiv berechnen <span class=\"ks-badge\">ohne Winkel<\/span><\/div>\n <\/div>\n <div class=\"step-body\">\n <p class=\"desc\">F\u00fcr die Scheinleistung ohne Winkelberechnung (Effektivwerte):<\/p>\n\n <div class=\"formula-full\" style=\"margin-top:0;\">\n <div class=\"label\">Effektivspannung<\/div>\n U<span class=\"sub\">effektiv<\/span> = 400 V\n <\/div>\n\n <div class=\"formula-full\">\n <div class=\"label\">Effektivstrom<\/div>\n <span style=\"display:inline-flex; align-items:center; gap:0; vertical-align:middle;\">\n I<span class=\"sub\">effektiv<\/span> = \n <span style=\"display:inline-flex; align-items:stretch;\">\n <span style=\"font-size:2em; line-height:1; font-weight:300; transform:scaleY(0.85); display:inline-block;\">\u221a<\/span>\n <span style=\"display:inline-flex; flex-direction:column; border-top:1.5px solid var(--text); padding:2px 6px 0; justify-content:center;\">\n <span class=\"frac\">\n <span class=\"num\" style=\"border-bottom:none; white-space:nowrap;\">|I<span class=\"sub\">1<\/span>|<span class=\"sup\">2<\/span> + |I<span class=\"sub\">2<\/span>|<span class=\"sup\">2<\/span> + |I<span class=\"sub\">3<\/span>|<span class=\"sup\">2<\/span><\/span>\n <span class=\"den\" style=\"text-align:center;\">3<\/span>\n <\/span>\n <\/span>\n <\/span>\n <\/span>\n <\/div>\n\n <div class=\"formula-full\">\n <div class=\"label\">Scheinleistung effektiv<\/div>\n S<span class=\"sub\">effektiv<\/span> = U<span class=\"sub\">effektiv<\/span> \u00b7 I<span class=\"sub\">effektiv<\/span>\n <\/div>\n <\/div>\n <\/div>\n\n \n <div class=\"step\">\n <div class=\"step-header\">\n <div class=\"step-num\">11<\/div>\n <div class=\"step-title\">Wirkungsgrad \u03b7 & Leistungsfaktor cos \u03c6<\/div>\n <\/div>\n <div class=\"step-body\">\n <div class=\"formula-grid-2\">\n <div class=\"formula-card\">\n <div class=\"formula-label\">Wirkungsgrad \u03b7 [%]<\/div>\n <div class=\"formula-eq\">\n \u03b7 =\n <span class=\"frac\">\n <span class=\"num\">P<span class=\"sub\">ab<\/span><\/span>\n <span class=\"den\">P<span class=\"sub\">zu<\/span><\/span>\n <\/span>\n =\n <span class=\"frac\">\n <span class=\"num\">P<span class=\"sub\">ges<\/span><\/span>\n <span class=\"den\">S<span class=\"sub\">effektiv<\/span><\/span>\n <\/span>\n <\/div>\n <\/div>\n <div class=\"formula-card\">\n <div class=\"formula-label\">Leistungsfaktor<\/div>\n <div class=\"formula-eq\">cos \u03c6 = cos(\u2220S<span class=\"sub\">ges<\/span>)<\/div>\n <\/div>\n <\/div>\n <div class=\"info-box\">\n <strong>Hinweis:<\/strong> \u03b7 in % angeben \u00b7 cos \u03c6 ist der Winkel von S<sub>ges<\/sub> im Exponentialformat\n <\/div>\n <\/div>\n <\/div>\n\n<\/div>\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>Sternschaltung \u2013 Formeln 1 Z1, Z2, Z3 bestimmen Exponential Impedanzen jedes Strangs im Exponentialformat bestimmen: Strang 1 Z1 = |Z1| \u00b7 ej\u03c6\u2081 Strang 2 Z2 = |Z2| \u00b7 ej\u03c6\u2082 Strang 3 Z3 = |Z3| \u00b7 ej\u03c6\u2083 2 Strom im Neutralleiter berechnen IN = UR Z1 + US Z2 + UT […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_themeisle_gutenberg_block_has_review":false,"footnotes":""},"class_list":["post-150","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/fseschueler19.bplaced.net\/wordpress\/wp-json\/wp\/v2\/pages\/150","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fseschueler19.bplaced.net\/wordpress\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/fseschueler19.bplaced.net\/wordpress\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/fseschueler19.bplaced.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fseschueler19.bplaced.net\/wordpress\/wp-json\/wp\/v2\/comments?post=150"}],"version-history":[{"count":4,"href":"https:\/\/fseschueler19.bplaced.net\/wordpress\/wp-json\/wp\/v2\/pages\/150\/revisions"}],"predecessor-version":[{"id":200,"href":"https:\/\/fseschueler19.bplaced.net\/wordpress\/wp-json\/wp\/v2\/pages\/150\/revisions\/200"}],"wp:attachment":[{"href":"https:\/\/fseschueler19.bplaced.net\/wordpress\/wp-json\/wp\/v2\/media?parent=150"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}