Chapter 13, Problem 1P

For the sinusoidal waveform in Fig. 13.85:

a. What is the peak value?

b. What is the instantaneous value at 15 ms and at 20 ms?

c. What is the peak-to-peak value of the waveform?

d. What is the period of the waveform?

e. How many cycles are shown?

To determine

(a)

Peak value of sinusoidal signal.

Answer to Problem 1P

The peak value is $10\text{V}$.

Explanation of Solution

Calculation:

Peak value is the maximum value of an alternating quantity over one cycle duration.

So peak value is $10\text{V}$.

Conclusion:

Thus, peak value is $10\text{V}$.

To determine

(b)

Instantaneous value at $15\text{ms}$ and $20\text{ms}$.

Answer to Problem 1P

The Instantaneous value at $15\text{ms}$ is $-10\text{V}$ and instantaneous value at $20\text{ms}$ is $0\text{V}$.

Explanation of Solution

Calculation:

Instantaneous value is the valueof an alternating quantity at a particular value of time in a cycle.

So Instantaneous value at $15\text{ms}$ is $-10\text{V}$ and instantaneous value at $20\text{ms}$ is $0\text{V}$.

Conclusion:

Thus, Instantaneous value at $15\text{ms}$ is $-10\text{V}$ and instantaneous value at $20\text{ms}$ is $0\text{V}$.

To determine

(c)

Peak-to-peak value of sinusoidal signal.

Answer to Problem 1P

The peak-to-peak value of sinusoidal signal is $20\text{V}$.

Explanation of Solution

Calculation:

Peak to peak value is the difference in the value of positive peak and negative peak of a waveform.

Write the expression for peak to peak value.

  $v_{p-p}=v_1-v_2$  ............(1)

Here, $v_{p-p}$ is peak to peak value of voltage, $v_1$ is value of positive peak and $v_2$ is value of negative peak.

Substitute $10\text{V}$ for $v_1$ and $-10\text{V}$ for $v_2$ in equation (1).

  $\begin{array}{c}{v}_{p-p}=\left(10\text{V}\right)-\left(-10\text{V}\right)\\ =20\text{V}\end{array}$

Conclusion:

Thus, Peak-to-peak value of sinusoidal signal is $20\text{V}$.

To determine

(d)

Value of period of the waveform.

Answer to Problem 1P

The value of period of the wave form is $20\text{ms}$.

Explanation of Solution

Calculation:

Period is the time taken by a waveform to complete its one cycle.

Waveform completes its one cycle in $20\text{ms}$ therefore value of period is $20\text{ms}$

Conclusion:

Thus, value of period of the wave form is $20\text{ms}$.

To determine

(e)

Value of number of cycles.

Answer to Problem 1P

The value of total number of cycle is $2$.

Explanation of Solution

Calculation:

There is $2$ complete cycle. Therefore total number of cycle is $2$.

Conclusion:

Thus, value of total number of cycle is $2$.