Question

In the given circuit the R.M.S. values of voltages across the capacitor $C$ , inductor $L$ and resistor $R_1$ are $12V$ , $10V$ and $5V$ respectively. Then the peak voltage across $R_2$ is

• A. $7\sqrt{2}V$
• B. $\sqrt{69}V$
• C. $\sqrt{138}V$
• D. none of these

Answer 1

Answer: (C)

In parallel combination each branch should have equal potential but in AC circuit in a branch,
$V_{eff}=\sqrt{V_R^2+{\left(V_c-V_L\right)}^2}$
$V_C^2+V_{R1}^2=V_L^2+V_{R2}^2$
$\Rightarrow 12^2+5^2=10^2+V_{R2}^2$
$\Rightarrow {\left(V_{R2}\right)}_{rms}=\sqrt{69}$
$V_{peak}=\sqrt{2}{V}_{rms}$
$\therefore {\left(V_{R2}\right)}_{\text{peak }}=\sqrt{138}V$