Question

Calculate the quality factor of a series LCR circuit with L = 4.0 H, C = 1, μF and R = 20 Ω.

Mention the significance of quality factor in LCR circuit.

Answer 1

The quality factor (Q) of a series LCR circuit is mathematically given as

`Q =1/R sqrt(L/C)`

here

R = resistance = 20Ω

L = inductance = 4.0 H

C = Capacitance = 1μF = 10⁻⁶F

So, the quality factor relation can be rewritten as

`Q = 1/20 xx (9/(10^-6))^(1/2)`

or

`Q = 1/20 xx 2 xx 10^3`

So, the quality factor of the given series LCR combination is

`Q=100`

The quality factor is defined as the ratio of voltage drop across the inductor or capacitor to that of applied voltage. It measures the sharpness of resonance of an LCR circuit.