In an RC circuit, what does the time constant represent?

The time constant in an RC (resistor-capacitor) circuit is a crucial concept that quantifies how quickly the circuit responds to changes in voltage or current. It is defined as the product of the resistance (R) and the capacitance (C), represented mathematically as τ = R × C.

This time constant is especially important for understanding how the voltage across the capacitor evolves over time when charging or discharging. During the discharge phase, for instance, the time constant indicates how long it takes for the voltage across the capacitor to fall to approximately 36.8% of its initial value. This behavior reflects the rate of discharge of the capacitor in the circuit.

When the circuit is powered off, the charge stored in the capacitor will decrease exponentially over time, and the time constant directly influences the speed of this process. A larger time constant means a slower discharge, while a smaller time constant indicates a faster discharge. Thus, the time constant serves as a key metric for predicting the rate at which the circuit discharges its stored energy.

While the other choices relate to circuit behavior, they do not accurately define the time constant itself. The time for current to stabilize or the time for voltage to reach maximum is not solely dictated by