Halliday, Resnick & Walker — Induction and Inductance: Problem 8

8 Suppose the emf of the battery in the circuit shown in Fig. 30-16 varies with time \( t \) so that the current is given by \( i(t) = 3.0 + 5.0t \), where \( i \) is in amperes and \( t \) is in seconds. Take \( R = 8.0 \, \Omega \) and \( L = 6.0 \, \text{H} \), and find an expression for the battery emf as a function of \( t \). (Hint: Apply the loop rule.)