Question

The quality factor of a series LCR resonant circuit is 75. If the resistance is decreased by 50% and the inductance is increased by 100%, then the quality factor of the circuit is:

• A. \( 150 \)
• B. \( 150 \sqrt{2} \)
• C. \( 300 \)
• D. \( 300 \sqrt{2} \)

Hint:

The quality factor of an LCR circuit is influenced by both resistance and inductance. A decrease in resistance increases the quality factor, while an increase in inductance also increases it.

Answer 1

The Correct Option is B

The quality factor \( Q \) of an LCR circuit is given by: \[ Q = \frac{1}{R} \sqrt{\frac{L}{C}} \] When the resistance is decreased by 50% and the inductance is increased by 100%, the new quality factor will change as follows: Since resistance decreases by 50%, the new resistance \( R' = \frac{R}{2} \). The inductance is increased by 100%, so the new inductance \( L' = 2L \). Thus, the new quality factor \( Q' \) is: \[ Q' = \frac{1}{R'} \sqrt{\frac{L'}{C}} = \frac{2}{R} \sqrt{\frac{2L}{C}} = 150 \sqrt{2} \]