Chapter 3.7, Problem 6P

Problems 1 through 6 deal with the RL circuit of Fig. 3.7.7, a series circuit containing an inductor with an inductance of L henries, a resistor with a resistance of R ohms, and a source of electromotive force (emf), but no capacitor In this case Eq. (2) reduces to the linear first-order equation FIGURE 3.7.7. The circuit for Problems 1 through 6. $LI\text{'}+RI=E\left(t\right)$

In the circuit of Fig. 3.7.7, with the switch in position 1, take $L=1,R=10,\text{and}E\left(t\right)=30\cos 60t+40\sin 60t$. (a) Substitute $I_{\text{sp}}\left(t\right)=A\cos 60t+B\sin 60t$ and then determine A and B to find the steady-state current $I_{\text{sp}}$ in the circuit. (b) Write the solution in the form $I_{\text{sp}}\left(t\right)=c\cos \left(\omega t-\alpha \right)$ .