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Alternating Current question

2004 · Shift 0 · Q152
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Alternating Current question

2004 · Shift 0 · Q152

JEE MainPhysicsAlternating CurrentMCQ+4 / −1
In a LCRLCRLCR circuit capacitance is changed from CCC to 2C2C2C. For the resonant frequency to remain unchaged, the inductance should be changed from LLL to
  1. A
    L/2L/2L/2
  2. B
    2L2L2L
  3. C
    4L4L4L
  4. D
    L/4L/4L/4
View written solutionFree

Correct answer: A

  1. The resonant frequency of an LCRLCRLCR circuit is
f0=12πLC. f_0 = \frac{1}{2\pi\sqrt{LC}}.f0​=2πLC​1​.
  1. For the resonant frequency to remain unchanged, the quantity LCLCLC must remain constant.

Initially,

LC=L⋅C.LC = L\cdot C.LC=L⋅C.

After changing the capacitance from CCC to 2C2C2C, let the new inductance be L′L'L′. Then for resonance to remain the same,

L′⋅2C=LC.L' \cdot 2C = LC.L′⋅2C=LC.
  1. Solving for L′L'L′:
L′=LC2C=L2.L' = \frac{LC}{2C} = \frac{L}{2}.L′=2CLC​=2L​.
  1. Therefore, the inductance should be changed from LLL to
L2.\boxed{\frac{L}{2}}.2L​​.
  1. Checking options:
  • A: L/2L/2L/2 ✅
  • B: 2L2L2L ❌
  • C: 4L4L4L ❌
  • D: L/4L/4L/4 ❌

Hence, the correct option is A.

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