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A capacitor C discharges through resistance R with time constant tau (so tau = RC). The same R and C are now connected in series across an AC source of angular frequency omega = 1/tau. Find the impedance of the RC series circuit.

1. R / sqrt(2)
2. R
3. sqrt(2) * R
4. 2*R

Correct answer: sqrt(2) * R

Solution

tau = RC, so C = tau/R. At omega = 1/tau: X_C = 1/(omega*C) = 1/(1/tau * tau/R) = R. Series impedance Z = sqrt(R² + X_C²) = sqrt(R² + R²) = R*sqrt(2).

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