In a series LCR circuit, the inductance, capacitance and resistance are $L=100~\mathrm{mH}$, $C=100~\mu\mathrm{F}$ and $R=10~\Omega$ respectively. They are connected to an AC source of voltage 220 V and frequency of 50 Hz. The approximate value of current in the circuit will be $\_\_\_\_$ A.

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Alternating Current

In a series LCR circuit, the inductance, capacitance and resistance are

L = 100 mH

C = 100 μ F

and

R = 10 Ω

respectively. They are connected to an AC source of voltage 220 V and frequency of 50 Hz. The approximate value of current in the circuit will be

____

Answer: 22

Calculate the reactances:

X_{L} = ω L = 2 π \times 50 \times 0.1 = 10 π Ω

X_{C} = \frac{1}{ω C} = \frac{1}{2 π \times 50 \times 100 \times 1 0 ^{- 6}} = \frac{100}{π} Ω

The impedance:

Z = (X_{L} - X_{C})^{2} + R^{2} = (10 π - \frac{100}{π})^{2} + 1 0^{2}

Since

10 π \approx 31.4

and

\frac{100}{π} \approx 31.8

, we have

X_{L} - X_{C} \approx - 0.4

, so:

Z \approx 0.16 + 100 \approx 10 Ω

Current:

i = \frac{V}{Z} = \frac{220}{10} = 22 A

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Integer answer