An RLC series resonance circuit has a resonance frequency of (5000/2π) Hz and impedance at resonance is 56 Ω. Find the value of the inductance if the Q-factor is 25.
Question
An RLC series resonance circuit has a resonance frequency of (5000/2π) Hz and impedance at resonance is 56 Ω. Find the value of the inductance if the Q-factor is 25.
Solution
The Q-factor of a resonance circuit is given by the formula:
Q = (Resonant frequency * L) / R
Where:
- Q is the Q-factor
- L is the inductance
- R is the resistance
We can rearrange this formula to solve for L:
L = (Q * R) / Resonant frequency
Given that the Q-factor is 25, the resistance is 56 Ω, and the resonant frequency is (5000/2π) Hz, we can substitute these values into the formula:
L = (25 * 56) / (5000/2π)
Solving this equation gives:
L = 0.177 H
So, the inductance of the circuit is approximately 0.177 Henries.
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