Question

In the given circuit, $V_C=50V$ and $R=50\Omega$. The values of $C$ and $V_R$ are

• A. $3.3\mu F,60V$
• B. $3.3\mu F,98V$
• C. $1.6\mu F,30V$
• D. $2\mu F,60V$

Answer 1

Answer: (B)

$V_C^2+V_R^2=V^2$
$50^2+V_R^2=V^2$
$V_R^2=110^2-50^2$
$V_R=\sqrt{110^2-50^2}$

$V_R=\sqrt{160\times 60}\simeq 98V$
Then, $I_v=\frac{98}{50}(\therefore R=50\Omega )$
Also, $I_v=\frac{110}{\sqrt{R^2+X_C^2}}$
$\Rightarrow \frac{98}{50}=\frac{110}{\sqrt{50^2+X_C^2}}$
Find $X_C$ and then use $X_c=\frac{1}{\omega C}$ to find $C$.
$C=3.3\mu F$