Question

Consider the following AC RLC circuit. The maximum voltage drop across the inductor is -

• A. $17.5\text{V}$
• B. $15.5\text{V}$
• C. $12.5\text{V}$
• D. $19.5\text{V}$

Answer 1

The correct option is C $12.5\text{V}$


Here,

$X_L=\omega L=100\times 0.5=50\Omega$

$X_C=\frac{1}{\omega C}=\frac{1}{100\times 200\times {10}^{-6}}=50\Omega$

The impedance is,

$Z=\sqrt{R^2+(X_C-X_L{)}^2}$

$\Rightarrow Z=\sqrt{{20}^2+(50-50{)}^2}=20\Omega$

Now,

$I_0=\frac{V_0}{Z}=\frac{5}{20}=\frac{1}{4}\text{A}$

So, the maximum voltage drop across the inductor is,

$V_{L_0}=I_0{X}_L=\frac{1}{4}\times 50=12.5\text{V}$

Hence, option $\left(C\right)$ is the correct answer.