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 ______
To determine the quality factor \( Q \) of an LCR circuit connected in series, we use the formula: \( Q = \frac{1}{R} \sqrt{\frac{L}{C}} \), where \( R \) is the resistance, \( L \) is the inductance, and \( C \) is the capacitance. First, substitute the given values: Resistance \( R = 100 \, \Omega \) Inductance \( L = 1 \, \text{H} \) Capacitance \( C = 6.25 \, \mu\text{F} = 6.25 \times 10^{-6} \, \text{F} \) Now, calculate \( \sqrt{\frac{L}{C}} \): \( \sqrt{\frac{1}{6.25 \times 10^{-6}}} = \sqrt{1.6 \times 10^{5}} \) \( = 400 \) Next, calculate the quality factor \( Q \): \( Q = \frac{1}{100} \times 400 = 4 \) The quality factor \( Q \) is 4, which fits within the range of 4 to 4 as expected.
