Question

In the following series $LCR$ circuit, find the peak value of source current $i_0$, voltage across capacitor $V_C$ and voltage across inductor $V_L$ at resonance, respectively.

• A. $5\text{A},100\text{V},100\text{V}$
• B. $2\text{A},100\text{V},200\text{V}$
• C. $10\text{A},20\text{V},30\text{V}$
• D. $5\text{A},50\text{V},50\text{V}$

Answer 1

The correct option is A $5\text{A},100\text{V},100\text{V}$

We know that, at resonance,

$X_L=X_C$

$\therefore Z=R=2\Omega$

Now, peak value of source current,

$i_0=\frac{V_0}{Z}=\frac{10}{2}=5\text{A}$

Voltage across inductor,

$V_L=i_0{X}_L=5\times 20=100\text{V}$

Voltage across capacitor,

$V_C=i_0{X}_C=5\times 20=100\text{V}$

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