展開する (1/R = 1/(R_{1)}+1/(R_{2)})*R^2

解

展開する

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

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

解答ステップ

(\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}})

分配法則を適用する:

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}

簡素化

\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}}