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Question: Answered & Verified by Expert
A circuit element X when connected to an AC supply of peak voltage 100 V gives a peak current of 5 A which is in phase with the voltage. A second element Y when connected to the same AC supply also gives the same value of peak current which lags behind the voltage by π2. If X and Y are connected in series to the same supply, what will be the rms value of the current in ampere?
PhysicsAlternating CurrentJEE MainJEE Main 2022 (29 Jul Shift 2)
Options:
  • A 102
  • B 52
  • C 52
  • D 52
Solution:
2310 Upvotes Verified Answer
The correct answer is: 52

As current is in phase with the applied voltage, element X should be resistive with R=V0I0=1005=20 Ω.

As current lags behind voltage by 90°, element Y should be inductive with XL=V0I0=1005=20 Ω

When X and Y are connector in series, 

Impedance, Z=XL2+R2=202+202=202 Ω

Now, peak current, I0=V0Z=100202=52 A

Thus, the rms value of current is Irms=I02=52 A

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