The angular frequency of alternating 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.

(C) 0.8 H and $250 \mu \mathrm{~F}$

(A) 0.8 H and $150 \mu \mathrm{~F}$

(B) 1.33 H and $250 \mu \mathrm{~F}$

(D) 1.33 H and $150 \mu \mathrm{~F}$

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Alternating Current

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

100 rad / s

. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

Answer: (C)

The switch in the

R^{'}

branch is open, so no current flows through

R^{'}

and the condenser, the

60 Ω

resistor and the coil carry one and the same current.

That current follows from the voltage marked across the resistor:

i = \frac{15}{60} = 0.25 A

The coil carries

20

V, so

X_{L} = \frac{20}{0.25} = 80 Ω

and

L = \frac{X _{L}}{ω} = \frac{80}{100} = 0.8

H.

The condenser carries

10

V, so

X_{C} = \frac{10}{0.25} = 40 Ω

and

C = \frac{1}{ω X _{C}} = \frac{1}{100 \times 40} = 2.5 \times 1 0^{- 4}

F.

The coil has inductance

0.8

H and the condenser has capacity

250 μ

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Single correct option