After one time constant, what percentage of the source voltage remains in a discharging capacitor?

When a capacitor discharges through a resistor, the voltage across the capacitor decreases exponentially over time. The time constant (often denoted as τ) is defined as the product of the resistance (R) and the capacitance (C) in the circuit, and it provides a measure of how quickly the capacitor will discharge.

After one time constant, the voltage across the discharging capacitor drops to approximately 36.8% of its initial value. This is derived from the formula for the voltage across a discharging capacitor:

[ V(t) = V_0 \cdot e^{-t/τ} ]

At ( t = τ ), the equation simplifies to:

[ V(τ) = V_0 \cdot e^{-1} ]

Since ( e^{-1} ) is approximately 0.3679, this results in about 36.8% of the initial voltage remaining after one time constant has elapsed. Understanding this concept is crucial in electrical engineering for analyzing and designing circuits that involve capacitors and resistors.