Define the time constant for an RL circuit and give its units.

Define the time constant for an RL circuit and give its units.

• A. τ = L/R; seconds
• B. τ = R/L; seconds
• C. τ = L R; seconds
• D. τ = L/R; milliseconds

Answer: (A)

The time constant for an RL circuit is determined by the inductance and resistance: it is the ratio L divided by R. This quantity sets how quickly the current responds after a change, because the current in a step-response grows toward its final value I_final = V/R according to i(t) ≈ I_final(1 − e^(−t/τ)). The units work out as henries divided by ohms, which equals seconds, so the time constant is measured in seconds. After a time equal to τ, the current has risen to about 63% of its final value, illustrating how τ governs the speed of the transient response. Expressions that swap R and L or multiply them don’t have the correct units for time, so they don’t represent a time constant. Therefore, τ = L/R with units of seconds correctly captures both the relation and the dimensions.

The time constant for an RL circuit is determined by the inductance and resistance: it is the ratio L divided by R. This quantity sets how quickly the current responds after a change, because the current in a step-response grows toward its final value I_final = V/R according to i(t) ≈ I_final(1 − e^(−t/τ)). The units work out as henries divided by ohms, which equals seconds, so the time constant is measured in seconds. After a time equal to τ, the current has risen to about 63% of its final value, illustrating how τ governs the speed of the transient response. Expressions that swap R and L or multiply them don’t have the correct units for time, so they don’t represent a time constant. Therefore, τ = L/R with units of seconds correctly captures both the relation and the dimensions.