Chapter 6.6, Problem 19E

To determine

Tofind:The equation for the instantaneous voltage.

Answer to Problem 19E

The equation for the instantaneous voltageis $V_R=120\sin \left(\frac{\pi }{30}t\right)$ .

Explanation of Solution

Given information:The graph is shown below.

  

Calculation:

From the graph it is clear that he amplitude of the function is 120.

The time for completion of one cycle is time period is,

  $\begin{array}{l}\frac{2\pi }{k}=60\\ k=\frac{\pi }{30}\end{array}$

There is no phase shift thus $c=0$ . And there is no vertical shift $h=0$ .

The equation ism

  $\begin{array}{l}{V}_R=A\sin \left(kt+c\right)+h\\ V_R=120\sin \left(\frac{\pi }{30}t+0\right)+0\\ V_R=120\sin \left(\frac{\pi }{30}t\right)\end{array}$

Thus, the equation for the instantaneous voltage is $V_R=120\sin \left(\frac{\pi }{30}t\right)$ .