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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?
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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.
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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