Question

In the given circuit the peak voltage across $C, L$ and $R$ are $30 \,V$, $110 \,V$ and $60\, V$ respectively. The rms value of the applied voltage is

• A. 100 V
• B. 200 V
• C. 70.7 V
• D. 141 V

Answer 1

Answer: (C)

$V_{0}=\sqrt{V_{R}^{2}+\left(V_{L}-V_{C}\right)^{2}}$
$=\sqrt{60^{2}+\left(110^{2}-30^{2}\right)}=100$
$V_{r m s}=\frac{V_{0}}{\sqrt{2}}=\frac{100}{\sqrt{2}}$
$=\frac{100}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}=100 \times \frac{\sqrt{2}}{2}$
$=50 \times 1.414=70.7 \,V$