Engineers call the number L/R the time constant of the RL circuit in Figure 9.9. The significance of the time constant is that the current will reach 95% of its final value within 3 time constants of the time the switch is closed (Figure 9.9). Thus, the time constant gives a built-in measure of how rapidly an individual circuit will reach equilibrium.

In Figure 9.9

a. Find the value of i in Equation (7) that corresponds to t = 3L/R and show that it is about 95% of the steady-state value I = V/R.

b. Approximately what percentage of the steady-state current will be flowing in the circuit 2 time constants after the switch is closed (i.e., when t = 2L/R)?

R 0 L R (1-e-R/L) 2/1/23/1/20 44/12 R