Chapter 6, Problem 23P

A parallel RL circuit is subjected to a sinusoidal voltage of frequency $120\pi \text{rad/s}$ as shown in Fig. P6.23. The currents $i_1\left(t\right)$ and $i_2\left(t\right)$ are given by

$i_1\left(t\right)=10\sin \left(120\pi t\right)\text{A}$ $i_2\left(t\right)=10\sin \left(120\pi t-\frac{\pi }{2}\right)\text{A}$.

1. Given that $i\left(t\right)=i_1\left(t\right)+i_2\left(t\right)$, write $i\left(t\right)$
2. in the form $i\left(t\right)=M\sin \left(120\pi t+\theta \right)$
3. ;in other words, find M and $\theta$.

(b)Suppose $i\left(t\right)=14.14\sin \left(120\pi t-\frac{\pi }{4}\right)\text{A}$. Determine the amplitude, frequency (in Hz), period (in seconds), phase shift (in degree), and time shift (in seconds). (c) Given your results of part (b), plot one cycle of the current $i\left(t\right)$, and clearly indicate the earliest time after $t=0$ at which it reaches its maximum value.