Chapter 5, Problem 5.1P

Consider the plot of the sinusoidal voltage $v\left(t\right)=V_m\cos \left(\omega t+\theta \right)$ shown in Figure 5.1 on page 216 and the following statements:

1. Stretches the sinusoidal curve vertically.

Compresses the sanuso.dal curve vertically.

Stretches the sinusoidal curve horizontally.

Compresses the sinusoidal curve horizontally.

Translates the sinusoidal curve to the right.

Translates the sinusoidal curve to the left.
Which statement best describes

a. Increasing the peak amplitude $V_m$ ?
b. Increasing the frequency f?
c. Decreasing $\theta$?
d. Decreasing the angular frequency w?
e. Increasing the period?

To determine

Change in sinusoidal voltage graph if peak amplitude is increased.

Answer to Problem 5.1P

Increasing the peak amplitude stretches the sinusoidal curve vertically.

Option (1).

Explanation of Solution

Given information:

Given sinusoidal voltage is

$v\left(t\right)=V_m\cos \left(\omega t+\theta \right)$

Calculation:

Graph of sinusoidal voltage is

From the graph, it is noted thatif peak amplitude V_m is increased, it stretches the sinusoidal curve vertically.

To determine

Change in sinusoidal voltage graph if frequency is increased.

Answer to Problem 5.1P

Increasing the frequency compresses the sinusoidal curve horizontally.

Option (4).

Explanation of Solution

Given information:

Given sinusoidal voltage is

$v\left(t\right)=V_m\cos \left(\omega t+\theta \right)$

Calculation:

Graph of sinusoidal voltage is

From the graph, it is noted that if the frequency is increased,the time period is reduced so that it compresses the sinusoidal curve horizontally.

To determine

Change in sinusoidal voltage graph if phase angle (theta) is decreased.

Answer to Problem 5.1P

Decreasing the phase angle (theta) translates the sinusoidal curve to the right.

Option (5).

Explanation of Solution

Given information:

Given sinusoidal voltage is

$v\left(t\right)=V_m\cos \left(\omega t+\theta \right)$

Calculation:

Graph of sinusoidal voltage is

From the graph, it is noted that if the phase angle (theta) is decreased, it translates the sinusoidal curve to the right.

To determine

Change in sinusoidal voltage graph if the angular frequency is decreased.

Answer to Problem 5.1P

Decreasing the angular frequency stretches the sinusoidal voltage graph horizontally.

Option (3).

Explanation of Solution

Given information:

Given sinusoidal voltage is

$v\left(t\right)=V_m\cos \left(\omega t+\theta \right)$

Calculation:

Graph of sinusoidal voltage is

From the graph, it is noted that if the angular frequency is decreased, it increases the time period of the curve,which means it stretches sinusoidal horizontally.

To determine

Change in sinusoidal voltage graph if the time period is increased.

Answer to Problem 5.1P

Increasing the time period stretches the sinusoidal voltage graph horizontally.

Option (3).

Explanation of Solution

Given information:

Given sinusoidal voltage is

$v\left(t\right)=V_m\cos \left(\omega t+\theta \right)$

Calculation:

Graph of sinusoidal voltage is

From the graph, it is noted that if time period is increased, it stretches the sinusoidal voltage graph horizontally.