Chapter 6, Problem 26P

Consider the RC circuit shown in Fig.P6.25, where the currents are $i_1\left(t\right)=100\cos \left(100\pi t+\frac{\pi }{4}\right)\text{mA}$ and $i_2\left(t\right)=500\cos \left(100\pi t+\frac{3\pi }{4}\right)\text{mA}$.

(a) Given that $i\left(t\right)=i_1\left(t\right)+i_2\left(t\right)$, write $i\left(t\right)$ in the form $i\left(t\right)=M\sin \left(100t+\varphi \right)\text{A}$ in other words, find M and $\varphi$.

(b) Suppose now that $i\left(t\right)=0.51\sin \left(100t+146.31°\right)\text{A}$. Determine the amplitude, frequency (in Hz), period (in seconds), phase shift (in degrees), and time shift (in seconds).

(c) Given your result 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.