Question

Find the peak current and the resonant frequency of the following circuit as shown in the figure.

• A. $0.2\text{A}$ and $100\text{Hz}$
• B. $2\text{A}$ and $50\text{Hz}$
• C. $2\text{A}$ and $100\text{Hz}$
• D. $0.2\text{A}$ and $50\text{Hz}$

Answer 1

The correct option is D $0.2\text{A}$ and $50\text{Hz}$


Peak current in the series LCR circuit,

$i=\frac{v_o}{Z}$

$\Rightarrow i=\frac{v_o}{\sqrt{(X_L-X_C{)}^2+R^2}}$

$\Rightarrow i=\frac{30}{\sqrt{{(100\times 100\times {10}^{-3}-\frac{1}{100\times 100\times {10}^{-6}})}^2+{120}^2}}$

$[X_L=\omega L$ and $X_C=\frac{1}{\omega C}]$

$\Rightarrow i=0.2\text{A}$

Now, resonance frequency,
$\omega =\frac{1}{\sqrt{LC}}$

$\Rightarrow \omega =\frac{1}{\sqrt{100\times {10}^{-3}\times 100\times {10}^{-6}}}\approx 316\text{rad/s}$

So, $f=\frac{\omega }{2\pi }=\frac{316}{2\times 3.14}\approx 50\text{Hz}$