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JEE MainPhysicsAlternating Current

In a series LCR circuit, the applied voltage and the resulting current are given by v(t) = V₀ ( t) and i(t) = I₀ ( t) respectively. The circuit consists of an inductor of 25 mH , a capacitor of 40 F and a resistor of 10 . If the average power dissipated in the circuit is 500 W , the value of the peak voltage V₀ is _________ V .

Correct answer

100

Step-by-step solution

From the given equations for voltage and current, the phase difference between them is zero. This implies that the circuit is in a state of resonance, so the total impedance of the circuit is purely resistive, Z = R = 10 . The average power dissipated in an AC circuit is given by P = V_ rms ^2 R . Substituting the given values: 500 = V_ rms ^2 10 V_ rms ^2 = 5000 V_ rms = 5000 = 50 2 V The peak voltage V₀ is related to the rms voltage by V₀ = 2 V_ rms . V₀ = 2 50 2 = 100 V . Answer: 100

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