Question

A series combination of resistor of resistance 100 Ω, inductor of inductance 1 H and capacitor of capacitance 6.25 µF is connected to an ac source. The quality factor of the circuit will be ______

Answer 1

Correct Answer: 4

The quality factor (\( Q \)) of a series RLC circuit is given by: \[ Q = \frac{1}{R} \sqrt{\frac{L}{C}}, \] where: 
\( R = 100 \, \Omega \), 
 \( L = 1 \, \text{H} \), 
 \( C = 6.25 \, \mu\text{F} = 6.25 \times 10^{-6} \, \text{F} \). 
Substitute the values: \[ Q = \frac{1}{100} \sqrt{\frac{1}{6.25 \times 10^{-6}}}. \] 
Simplify: \[ Q = \frac{1}{100} \sqrt{1.6 \times 10^5} = \frac{1}{100} \cdot 400 = 4. \] 
Final Answer: The quality factor is: \[ \boxed{4}. \]