After one time constant, a discharging capacitor will have what percentage of its initial charge?

After one time constant, a discharging capacitor will retain approximately 37% of its initial charge, which translates into a loss of around 63% of that charge. The concept of a time constant is integral to the behavior of capacitors in an RC (resistor-capacitor) circuit.

When a capacitor discharges, the voltage and charge decrease exponentially over time, defined mathematically by the equation Q(t) = Q0 * e^(-t/τ), where Q0 is the initial charge, t is time, and τ (tau) is the time constant given by the product of resistance (R) and capacitance (C) in the circuit.

At time t = τ, the mathematics shows that the charge remaining is Q(τ) = Q0 * e^(-1) ≈ 0.3679, which is about 37% of the original charge. Hence, after one time constant has elapsed, the percentage of the charge that has been lost is approximately 63%. This means the statement that after one time constant, the capacitor retains about 63% of its initial charge is correct.