Question

The angular frequency of alternating current in a $LCR$ circuit is $100\text{rad/s}$. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

• A. $0.8\text{H}$ and $250\mu \text{F}$
• B. $0.8\text{H}$ and $150\mu \text{F}$
• C. $1.33\text{H}$ and $250\mu \text{F}$
• D. $1.33\text{H}$ and $150\mu \text{F}$

Answer 1

The correct option is A $0.8\text{H}$ and $250\mu \text{F}$

As key is open. The redrawn circuit is shown in the figure.
The shown circuit is series $LCR$ circuit.

$\therefore V_R=i_{\text{rms}}R$

$\Rightarrow 15=i_{\text{rms}}\times 60$

$\Rightarrow i_{\text{rms}}=0.25\text{A}$

So,
$V_L=i_{\text{rms}}{X}_L$

$\Rightarrow V_L=i_{\text{rms}}\times \omega L$

$\Rightarrow 20=0.25\times 100\times L$

$\Rightarrow L=0.8\text{H}$

Further,

$V_C=i_{\text{rms}}{X}_C$

$\Rightarrow V_C=i_{\text{rms}}\times \frac{1}{\omega C}$

$\Rightarrow 10=0.25\times \frac{1}{100\times C}$

$\Rightarrow C=2.5\times {10}^{-4}\text{F}=250\mu \text{F}$