Question

If the effective voltage of the AC source is 200 V and it’s frequency is variable for the circuit shown, then

• A. The frequency at which power dissipate in resistor is maximum is 50 Hz.
• B. The frequency at which power dissipated in resistor is maximum is $\frac{25}{\pi }Hz$
  
• C. The frequency at which power dissipated across the resistor drops to half its maximum value is $\frac{45}{2\pi }Hz$
• D. The frequency at which power dissipated across the resistor drops to half its maximum value is $\frac{20}{\pi }Hz$

Answer 1

Answer: (B), (C)

The correct options are
B The frequency at which power dissipated in resistor is maximum is $\frac{25}{\pi }Hz$

C The frequency at which power dissipated across the resistor drops to half its maximum value is $\frac{45}{2\pi }Hz$

P is maximum at resonance $\Rightarrow \omega =\frac{1}{\sqrt{LC}}$
$f=\frac{1}{2\pi }\sqrt{10\times 40\times {10}^{-6}}=\frac{25}{\pi }Hz{Q}_{factor}=\frac{\omega }{2\Delta \omega }=\frac{\omega L}{R}\Rightarrow \Delta \omega =\frac{R}{2L}=\frac{100}{20}=5\Delta f=\frac{45}{2\pi }$