The current waveform in Fig. 6.80 flows through a 3-H inductor. Sketch the voltage across the inductor over the interval 0 < t < 6 s.
Figure 6.80
For Prob. 6.58.
Sketch the voltage across the inductor over the interval
Explanation of Solution
Given data:
The value of the inductor
Refer to Figure 6.80 in the textbook.
Formula used:
Write the expression to calculate the straight line equation for two points
Refer to Figure 6.80 in the textbook.
From the given graph, substitute
Write the expression to calculate the voltage across the inductor.
Here,
Calculation:
The given current waveform is redrawn as Figure 1.
Refer to Figure 1, split up the time period as six divisions
Case (i):
The two points
Substitute
Simplify the equation to find
Case (ii):
The two points
Substitute
Simplify the equation to find
Case (iii):
The two points
Substitute
Simplify the equation to find
Case (iv):
The two points
Substitute
Simplify the equation to find
Case (v):
The two points
Substitute
Simplify the equation to find
Case (vi):
The two points
Substitute
Simplify the equation to find
Therefore, the current function of the signal in Figure 1 is,
For
Substitute
For
Substitute
For
Substitute
For
Substitute
For
Substitute
For
Substitute
The expression of the voltage
From the voltage expression, the signal is drawn in Figure 2.
Conclusion:
Thus, the voltage across the inductor over the interval
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Chapter 6 Solutions
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