erweitern (1/R = 1/(R_{1)}+1/(R_{2)})*R^2

Lösung

erweitern

(\frac{1}{R} = \frac{1}{R _{1}} + \frac{1}{R _{2}}) \cdot R^{2}

R = \frac{1}{R _{1}} + \frac{R ^{2}}{R _{2}}

Schritte zur Lösung

(\frac{1}{R} = \frac{1}{R _{1}} + \frac{1}{R _{2}}) R^{2}

= R^{2} (= \frac{1}{R} \cdot \frac{1}{R _{1}} + \frac{1}{R _{2}})

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = R^{2}, b = \frac{1}{R} = \frac{1}{R _{1}}, c = \frac{1}{R _{2}}

R^{2} \frac{1}{R} = \frac{1}{R _{1}} + R^{2} \frac{1}{R _{2}}

\frac{1}{R} R^{2} = \frac{1}{R _{1}} + \frac{1}{R _{2}} R^{2}

Vereinfache

\frac{1}{R} R^{2} = \frac{1}{R _{1}} + \frac{1}{R _{2}} R^{2} : R = \frac{1}{R _{1}} + \frac{R ^{2}}{R _{2}}

R = \frac{1}{R _{1}} + \frac{R ^{2}}{R _{2}}

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