Concept explainers
The current waveform depicted in Fig. 2.29 is characterized by a period of 4 s. (a) What is the average value of the current over a single period? (b) Compute the average current over the interval 1 < t < 3 s. (c) If q(0) = 1C, sketch q(t), 0 < t < 4 s.
FIGURE 2.29 An example of a time-varying current.
(a)
Find the average value of the given current waveform in Figure 2.29 over the period of 4 s.
Answer to Problem 21E
The average value of the given current waveform over the period of 4 s is
Explanation of Solution
Given data:
Refer to Figure 2.29 in textbook for the time-varying current with the period of 4 s.
Formula used:
Write the formula to find the average value of a function of current over a period as,
Here,
T is the time period.
Calculation:
From the given current waveform in Figure 2.29, the function of current
For the period of
For the period of
For the period of
For the period of
Therefore, the final function of current
The average value of current
Reduce the equation as follows.
Conclusion:
Thus, the average value of the given current waveform over the period of 4 s is
(b)
Find the average current of the waveform over the period of
Answer to Problem 21E
The average current of the waveform over the period of
Explanation of Solution
Given data:
Refer to part (a).
Formula used:
Write the formula to find the average value of a function of current over a period of
Here,
Calculation:
Write the function of current
Now, the average current of
Conclusion:
Thus, the average current of the waveform over the period of
(c)
Sketch the waveform for the charge
Explanation of Solution
Given data:
Refer to part (a).
The initial charge
Formula used:
Write the expression for the relation between charge
Integrate the above equation on both sides.
Calculation:
Using the function of
For
Substitute 3 A for
Substitute 1 C for
Substitute 1 for
For
For the period of
Substitute –1 A for
Substitute 4 C for
Substitute 2 for
For
For the period of
Substitute 1 A for
Substitute 3 C for
Substitute 3 for
For
For the period of
Substitute 0 A for
Substitute 4 C for
Therefore, the charge
Table 1 shows for
Table 1
t in seconds | |
0 | 1 |
1 | 4 |
2 | 2 |
3 | 4 |
4 | 4 |
Figure 1 shows the charge (C) vs time (s) waveform.
Conclusion:
Thus, the waveform for the charge
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Chapter 2 Solutions
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