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Alternating Current question

2022 · 26 Jul · Shift 1 · Q69
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Alternating Current question

2022 · 26 Jul · Shift 1 · Q69

JEE MainPhysicsAlternating CurrentNumerical+4 / −1
The effective current I in the given circuit at very high frequencies will be ‾\underline{\hspace{2cm}}​ A. JEE Main 2022 (Online) 26th July Morning Shift Physics - Alternating Current Question 73 English
Numerical answer
View written solutionFree

Correct answer: 44

  1. Behavior at very high frequency

At very high frequency:

  • Inductive reactance: XL=ωL→∞X_L = \omega L \to \inftyXL​=ωL→∞
    So the inductor behaves like an open circuit.
  • Capacitive reactance: XC=1ωC→0X_C = \dfrac{1}{\omega C} \to 0XC​=ωC1​→0
    So the capacitor behaves like a short circuit.

Thus, in the given AC circuit, we replace:

  • each inductor by an open branch,
  • each capacitor by a wire.
  1. Reduction of the circuit

After making these replacements, the circuit reduces to a purely resistive network.
From the given arrangement, the equivalent resistance at very high frequency becomes

Req=5 ΩR_{\text{eq}} = 5\ \OmegaReq​=5 Ω

  1. Effective current

The source effective voltage is

Vrms=220 VV_{\text{rms}} = 220\ \text{V}Vrms​=220 V

Hence the effective current is

I=VrmsReq=2205=44 AI = \frac{V_{\text{rms}}}{R_{\text{eq}}} = \frac{220}{5} = 44\ \text{A}I=Req​Vrms​​=5220​=44 A

  1. Final answer

Therefore, the effective current at very high frequencies is

44 A\boxed{44\ \text{A}}44 A​

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