What is the time constant in an RC circuit?

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Multiple Choice

What is the time constant in an RC circuit?

In an RC circuit, the time constant is the product of resistance and capacitance. This value, often written as tau (τ), sets the exponential time scale over which the capacitor charges or discharges. Specifically, when charging, the capacitor voltage follows v_C(t) = V_final (1 − e^(−t/RC)). After one time constant (t = RC), the voltage reaches about 63.2% of its final value. The current decays as i(t) = (V_source/R) e^(−t/RC); after one time constant, it drops to about 36.8% of its initial value. So the defining quantity is the RC product, which is why the correct answer is the product of resistance and capacitance. The percentages describe what happens after one time constant, not the defining measure itself.

In an RC circuit, the time constant is the product of resistance and capacitance. This value, often written as tau (τ), sets the exponential time scale over which the capacitor charges or discharges.

Specifically, when charging, the capacitor voltage follows v_C(t) = V_final (1 − e^(−t/RC)). After one time constant (t = RC), the voltage reaches about 63.2% of its final value. The current decays as i(t) = (V_source/R) e^(−t/RC); after one time constant, it drops to about 36.8% of its initial value.

So the defining quantity is the RC product, which is why the correct answer is the product of resistance and capacitance. The percentages describe what happens after one time constant, not the defining measure itself.

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