A series LCR circuit consists of $R=80 \Omega$, $X_L=100 \Omega$, and $X_C=40 \Omega$. The input voltage is $2500 \cos (100 \pi t)$ V. The amplitude of current, in the circuit, is ______ A.

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Alternating Current

A series LCR circuit consists of

R = 80Ω

X_{L} = 100Ω

, and

X_{C} = 40Ω

. The input voltage is

2500 cos (100 π t)

V. The amplitude of current, in the circuit, is ______ A.

Answer: 25

In a series LCR circuit the current is opposed by the impedance

Z = R^{2} + (X_{L} - X_{C})^{2}

. Here

Z = 8 0^{2} + (100 - 40)^{2} = 6400 + 3600 = 10000 = 100 Ω

. The applied voltage

2500 cos (100 π t)

has peak value

2500 V

, so the peak current is

\frac{V _{0}}{Z} = \frac{2500}{100}

, which is

25 A

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Integer answer