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Alternating Current question

2021 · 17 Mar · Shift 2 · Q51
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Alternating Current question

2021 · 17 Mar · Shift 2 · Q51

JEE MainPhysicsAlternating CurrentMCQ+4 / −1
What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved?
  1. A
    Both, inducting reactance and current will be doubled.
  2. B
    Inductive reactance will be doubled and current will be halved.
  3. C
    Both, inductive reactance and current will be halved.
  4. D
    Inductive reactance will be halved and current will be doubled.
View written solutionFree

Correct answer: D

  1. Formula for inductive reactance

For a pure inductor, the inductive reactance is XL=ωL=2πfLX_L = \omega L = 2\pi f LXL​=ωL=2πfL So, XLX_LXL​ is directly proportional to frequency fff.

  1. If frequency is halved

Let the initial frequency be fff. Then new frequency is f′=f2f' = \frac{f}{2}f′=2f​

Now, XL′=2π(f2)L=12(2πfL)=XL2X_L' = 2\pi \left(\frac{f}{2}\right)L = \frac{1}{2}(2\pi fL) = \frac{X_L}{2}XL′​=2π(2f​)L=21​(2πfL)=2XL​​ So, inductive reactance is halved.

  1. Current in a purely inductive AC circuit

Current is given by I=VXLI = \frac{V}{X_L}I=XL​V​ for a fixed applied voltage VVV.

Since XLX_LXL​ becomes half, I′=VXL/2=2VXL=2II' = \frac{V}{X_L/2} = 2\frac{V}{X_L} = 2II′=XL​/2V​=2XL​V​=2I So, current is doubled.

  1. Check options
  • A: Both doubled →\rightarrow→ Incorrect
  • B: Reactance doubled, current halved →\rightarrow→ Incorrect
  • C: Both halved →\rightarrow→ Incorrect
  • D: Reactance halved, current doubled →\rightarrow→ Correct

Therefore, the correct answer is D\boxed{\text{D}}D​

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