A series combination of resistor of resistance 100 $\Omega$, inductor of inductance 1 H and capacitor of capacitance $6.25 \mu \mathrm{~F}$ is connected to an ac source. The quality factor of the circuit will be \_\_\_\_.

JEE Main · 2023 · 08 Apr 2023 · Shift 2 · Alternating Current

A series combination of resistor of resistance 100

Ω

, inductor of inductance 1 H and capacitor of capacitance

6.25 μ F

is connected to an ac source. The quality factor of the circuit will be ____.

Answer: 4

The quality factor of a series

R L C

circuit at resonance is

Q = \frac{ω _{0} L}{R}

with

ω_{0} = \frac{1}{L C}

. Here

ω_{0} = \frac{1}{( 1 ) ( 6.25 \times 1 0 ^{- 6} )} = \frac{1}{2.5 \times 1 0 ^{- 3}} = 400 rad s^{- 1}

. Hence

Q = \frac{( 400 ) ( 1 )}{100}

. The quality factor of the circuit is

4

JEE Main · 2023 · 08 Apr 2023 · Shift 2 · Integer answer