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In an L-C-R circuit inductance is changed from L to L/2. To keep the same resonance frequency, C should be changed to
  • a)
    2C
  • b)
    C/2
  • c)
    4C
  • d)
    C/4
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In an L-C-R circuit inductance is changed from L to L/2. To keep the s...
Solution:

Resonance frequency in an LCR circuit is given by

f = 1/2π √(1/LC)

To keep the same resonance frequency, C should be changed to 2C when inductance is changed from L to L/2.

Explanation:

Given that the inductance is changed from L to L/2.

Resonance frequency, f = 1/2π √(1/LC)

When L is changed to L/2, to keep the same resonance frequency, the capacitance should be changed.

Let C' be the new capacitance.

The new resonance frequency is

f' = 1/2π √(1/L (C/2))

= 1/2π √(2/LC)

For f' to be equal to f,

1/2π √(2/LC) = 1/2π √(1/LC)

√2 = √(C/C')

C' = C/2

Therefore, to keep the same resonance frequency, C should be changed to 2C when inductance is changed from L to L/2.
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In an L-C-R circuit inductance is changed from L to L/2. To keep the same resonance frequency, C should be changed toa)2Cb)C/2c)4Cd)C/4Correct answer is option 'A'. Can you explain this answer?
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