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A series RL coil (high Q) operates at rated voltage V and specified frequency f0. When the frequency is doubled to 2f0 (at the same rated voltage), how are the quality factor Q and the active power P affected?

1. P is doubled, Q is halved
2. P is halved, Q is doubled
3. P remains constant but Q increases 4 times
4. P decreases 4 times but Q is doubled

Correct answer: P decreases 4 times but Q is doubled

Solution

For a series RL circuit: Q = omega*L/R. When omega doubles, Q doubles (R and L unchanged). Impedance Z = sqrt(R² + (omega*L)²). At high Q, omega*L >> R, so Z approximately = omega*L. Active power P = V²*R/Z² approximately V²*R/(omega*L)². When omega doubles: P_new approximately V²*R/(2*omega*L)² = P/4. So P decreases 4 times and Q doubles.

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