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By what percentage should the impedance in an AC series circuit be increased so that the power factor changes from \(\tfrac{1}{2}\) to \(\tfrac{1}{4}\), when \(R\) is constant?

1. 200%
2. 100%
3. 50%
4. 400%

Correct answer: 100%

Solution

For a series AC circuit, power factor \(\cos\phi = R/Z\). If \(R\) is constant, then \(Z\propto 1/\cos\phi\). When the power factor changes from \(1/2\) to \(1/4\), the impedance doubles, so the increase is 100%.

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