Chapter 13.7, Problem 22PPS

a.

To determine

To find: Equation for the Voltage $V$ as a function of time $t$

Answer to Problem 22PPS

Equation of given situation is

  $V=165\cos 100\pi t$

Explanation of Solution

Given information:

Frequency $=50$ cycles per second.

Voltage supply will varies between $-165$ volts and $165$ volt

At $t=0$ seconds, the current is $165$ volts.

Given

Frequency $=50$ cycles per second.

We know

Period $=\frac{1}{frequency}$

  $\Rightarrow$ Period $=\frac{1}{50}$

  $\Rightarrow$ Period $=0.02$

  $\begin{array}{l}\Rightarrow \frac{2\pi }{b}=0.02\\ \Rightarrow b=\frac{2\pi }{0.02}\\ \Rightarrow b=100\pi \end{array}$

Given

Voltage supply will varies between $-165$ volts and $165$ volt

It means Amplitude $=a=165$

At $t=0$ seconds, the current is $165$ volts.

It means Cosine function.

Therefore,

On substituting values

We get

  $\begin{array}{l}y=a\cos bt\\ \Rightarrow V=165\cos 100\pi t\end{array}$

Therefore,

Equation of given situation is

  $V=165\cos 100\pi t$

b.

To determine

To find: Graph of the function.

Explanation of Solution

Given information:

Frequency $=50$ cycles per second.

Voltage supply will varies between $-165$ volts and $165$ volt

At $t=0$ seconds, the current is $165$ volts.

Equation of given situation is

  $V=165\cos 100\pi t$

Graph of the function is