Question

A coil is designed for high Q performance at a rated voltage and a specified frequency. If the frequency is made twice the original and the coil is operated at the same rated voltage, then the active power P will be affected as ____________

(a) P is halved

(b) P remains unchanged

(c) P is doubled

(d) P decreases 4 times

The question was asked in final exam.

Origin of the question is Advanced Problems on Magnetically Coupled Circuits topic in division Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

Correct choice is (d) P decreases 4 times

Explanation: I1 = \(\frac{V}{\sqrt{R^2+  ω_1^2 L^2}} = \frac{V}{ω_1 L}\)

For a high current coil, ωL >> R

I2 = \(\frac{V_1}{2ω_1 L} = \frac{I_1}{2}\)

∴ P2 = R (\(\frac{I_1}{2}\))^2 = \(\frac{P_1}{4}\)

Therefore, P decreases 4 times.