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Alternating Current question

2021 · 25 Feb · Shift 2 · Q49
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  5. /2021 · 25 Feb · Shift 2 · Q49

Alternating Current question

2021 · 25 Feb · Shift 2 · Q49

JEE MainPhysicsAlternating CurrentMCQ+4 / −1
An LCR circuit contains resistance of 110 Ω\OmegaΩ and a supply of 220 V at 300 rad/s angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by 45 ∘^\circ∘. If on the other hand, only inductor is removed the current leads by 45 ∘^\circ∘ with the applied voltage. The rms current flowing in the circuit will be :
  1. A
    1 A
  2. B
    2.5 A
  3. C
    2 A
  4. D
    1.5 A
View written solutionFree

Correct answer: C

  1. Given data
  • Resistance: R=110 ΩR = 110\,\OmegaR=110Ω
  • Supply voltage: Vrms=220 VV_{\text{rms}} = 220\,\text{V}Vrms​=220V
  • Angular frequency: ω=300 rad/s\omega = 300\,\text{rad/s}ω=300rad/s

We need the rms current in the original series LCR circuit.


  1. Case 1: Capacitor removed

Then the circuit becomes a series RL circuit.

Given: current lags voltage by 45∘45^\circ45∘.

For an RL circuit,

tan⁡ϕ=XLR\tan \phi = \frac{X_L}{R}tanϕ=RXL​​

with ϕ=45∘\phi = 45^\circϕ=45∘.

So,

tan⁡45∘=XLR=1\tan 45^\circ = \frac{X_L}{R} = 1tan45∘=RXL​​=1 XL=R=110 ΩX_L = R = 110\,\OmegaXL​=R=110Ω
  1. Case 2: Inductor removed

Then the circuit becomes a series RC circuit.

Given: current leads voltage by 45∘45^\circ45∘.

For an RC circuit,

tan⁡ϕ=XCR\tan \phi = \frac{X_C}{R}tanϕ=RXC​​

where the phase magnitude is 45∘45^\circ45∘.

Thus,

tan⁡45∘=XCR=1\tan 45^\circ = \frac{X_C}{R} = 1tan45∘=RXC​​=1 XC=R=110 ΩX_C = R = 110\,\OmegaXC​=R=110Ω
  1. Original LCR circuit

In the original series LCR circuit,

Z=R2+(XL−XC)2Z = \sqrt{R^2 + (X_L - X_C)^2}Z=R2+(XL​−XC​)2​

But we found

XL=110 Ω,XC=110 ΩX_L = 110\,\Omega, \qquad X_C = 110\,\OmegaXL​=110Ω,XC​=110Ω

Hence,

XL−XC=0X_L - X_C = 0XL​−XC​=0

So the impedance is

Z=R2+02=R=110 ΩZ = \sqrt{R^2 + 0^2} = R = 110\,\OmegaZ=R2+02​=R=110Ω
  1. Current in the circuit

Using

Irms=VrmsZI_{\text{rms}} = \frac{V_{\text{rms}}}{Z}Irms​=ZVrms​​

we get

Irms=220110=2 AI_{\text{rms}} = \frac{220}{110} = 2\,\text{A}Irms​=110220​=2A
  1. Option check
  • A: 1 A1\,\text{A}1A ❌
  • B: 2.5 A2.5\,\text{A}2.5A ❌
  • C: 2 A2\,\text{A}2A ✅
  • D: 1.5 A1.5\,\text{A}1.5A ❌

Therefore, the correct answer is Option C.

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