The time constant formula for an RL circuit.

• A. t = L/R
• B. t = R/L
• C. t = LR
• D. t = R/L^2

Answer: (A)

In an RL circuit, the time constant sets the time scale over which the current responds to a voltage change. For a series RL circuit, the governing equation is L di/dt + iR = V. This can be written as di/dt + (R/L) i = V/L, which shows a first‑order system with a time constant τ = L/R.

This τ describes how quickly the current approaches its final value after a step in voltage: i(t) = (V/R) [1 − e^(−t/τ)]. It’s also the same τ that governs the exponential decay when the source is removed, i(t) = I0 e^(−t/τ).

Units check out: L in henries and R in ohms give L/R in seconds, as expected for a time constant. The other expressions don’t have the right units (for example, R/L has units of 1/seconds, not time) and don’t match the governing equation, so they don’t describe the circuit’s time response.