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A series R-C circuit is driven by an AC source of angular frequency omega = 500 rad/s. The impedance of the circuit equals R*sqrt(1.25). Find the time constant of the circuit (in milliseconds).

1. 4 ms
2. 2 ms
3. 1 ms
4. 8 ms

Correct answer: 4 ms

Solution

Z = sqrt(R² + Xc²) = R*sqrt(1.25) means R² + Xc² = 1.25*R², so Xc² = 0.25*R² and Xc = 0.5*R. Since Xc = 1/(omega*C), we have 1/(omega*C) = R/2, so R*C = 2/omega = 2/500 = 0.004 s = 4 ms. The time constant tau = R*C = 4 ms.

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