Question

Inductive resistance $25\Omega$ and capacitive resistance $75\Omega$ are connected across $250V$ mains in series. Find the rms potential difference across inductor and capacitor.

Answer 1

$V=i(R+j{X}_L)$

$\Rightarrow i=\frac{V}{\sqrt{R^2+X_L^2}}$

$i_{rms}=\frac{V_{rms}}{\sqrt{R^2+X_L^2}}$

$\Rightarrow i_{rms}=\frac{250/\sqrt{2}}{\sqrt{{25}^2+{75}^2}}=\frac{250}{79\sqrt{2}}$

$V_L=25i_{rms}=25\times \frac{250}{79\sqrt{2}}=\frac{79}{\sqrt{2}}=55.86V$

$V_R=75i_{rms}=167.58V$