For the electric circuit of Example 6, find how long it takes the current to reach 0.1 of the initial value of 0.750 A.

Data from Example 6

The electric current i in a circuit containing a resistance and an inductance (see Fig. 13.18) is given by ln(i/I ) = −Rt/L, where I is the current at t = 0, R is the resistance, t is the time, and L is the inductance. Calculate how long (in s) it takes i to reach 0.430 A, if I = 0.750A, R = 7.50Ω ,and L = 1.25H. Solving for t and then evaluating, we have

Therefore, the current changes from 0.750 A to 0.430 A in 0.0927 s.

t L In (i/I) R 1.25(In 0.430 In 0.750) 7.50 L(Ini - In 1) R = 0.0927