In an RC circuit, the time constant is defined as?

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Multiple Choice

In an RC circuit, the time constant is defined as?

The time constant is the RC product, which sets the exponential response rate of an RC circuit. It is the characteristic time scale over which charging or discharging occurs. In a charging circuit, the capacitor voltage approaches the supply toward its final value according to Vc(t) = Vsource(1 − e^(−t/RC)). After a time equal to RC, the capacitor voltage reaches about 63.2% of its final value, and the current decays to about 36.8% of its initial value (i(t) = (Vsource/R) e^(−t/RC)). This shows why RC is the time constant: it governs how quickly the circuit responds. The option stating the time for the current to reach 63.2% of maximum isn’t the definition, because the current decays from its initial value and reaches that percentage at a different time. The idea of discharging to zero in finite time is not correct for a capacitor, and the exact product RC is the defining quantity.

The time constant is the RC product, which sets the exponential response rate of an RC circuit. It is the characteristic time scale over which charging or discharging occurs. In a charging circuit, the capacitor voltage approaches the supply toward its final value according to Vc(t) = Vsource(1 − e^(−t/RC)). After a time equal to RC, the capacitor voltage reaches about 63.2% of its final value, and the current decays to about 36.8% of its initial value (i(t) = (Vsource/R) e^(−t/RC)). This shows why RC is the time constant: it governs how quickly the circuit responds.

The option stating the time for the current to reach 63.2% of maximum isn’t the definition, because the current decays from its initial value and reaches that percentage at a different time. The idea of discharging to zero in finite time is not correct for a capacitor, and the exact product RC is the defining quantity.

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