Question

A voltage of peak value 283V and varying frequency is applied to a series L, C, R combination in which \( R = 3 \, \Omega \), \( L = 25 \, \text{mH} \) and \( C = 400 \, \mu F \). The frequency (in Hz) of the source at which maximum power is dissipated in the above is

• A. 51.5
• B. 50.7
• C. 51.1
• D. 50.3

Hint:

Maximum power is dissipated in an LCR circuit when the frequency of the source is equal to the resonance frequency.

Answer 1

The Correct Option is D

Step 1: Condition for maximum power.
Maximum power in an LCR circuit is dissipated at resonance frequency, where \( L = 1 / C \). The resonance frequency \( f_0 \) is given by: \[ f_0 = \frac{1}{2 \pi \sqrt{LC}} \] Substituting the given values, we calculate the frequency.

Step 2: Conclusion.
Thus, the resonance frequency is approximately 50.3 Hz. Hence, the correct answer is option (D).

Final Answer: \[ \boxed{50.3 \, \text{Hz}} \]