The angular frequency of alternating current in a L-C-R circuit
Question:

The angular frequency of alterlating current in a L-C-R circuit is $100 \mathrm{rad} / \mathrm{s}$. The

components connected are shown in the figure. Find the value of inductance of the coil

and capacity of condenser.

1. (1) $0.8 \mathrm{H}$ and $250 \mu \mathrm{F}$

2. (2) $0.8 \mathrm{H}$ and $150 \mu \mathrm{F}$

3. (3) $1.33 \mathrm{H}$ and $250 \mu \mathrm{F}$

4. (4) $1.33 \mathrm{H}$ and $150 \mu \mathrm{F}$

Correct Option: 1

Solution:

(1)

Since key is open, circuit is series

$15=\mathrm{i}_{\mathrm{rms}}(60)$

$\therefore \mathrm{i}_{\mathrm{rms}}=\frac{1}{4} \mathrm{~A}$

Now, $20=\frac{1}{4} X_{\mathrm{L}}=\frac{1}{4}(\omega \mathrm{L})$

$\therefore \mathrm{L}=\frac{4}{5}=0.8 \mathrm{H}$

$\& 10=\frac{1}{4} \frac{1}{(100 C)}$

$C=\frac{1}{4000} F=250 \mu F$