Concept explainers
The voltage waveform in Fig. 6.46 is applied across a 55-μF capacitor. Draw the current waveform through it.
Figure 6.46
For Prob. 6.6.
Find the current waveform.
Explanation of Solution
Given data:
The value of the capacitor
Formula used:
Write the expression to calculate the straight line equation for two points
Refer to Figure 6.46 in the textbook.
From the given graph, substitute
Write the expression to calculate the current through the inductor.
Here,
Calculation:
The given voltage waveform is redrawn as Figure 1.
Refer to Figure 1, split up the time period as five divisions such as
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
Therefore, the voltage function of the signal in Figure 1 is,
For
Substitute
Simplify the equation to find
For
Substitute
For
Substitute
Simplify the equation to find
For
Substitute
For
Substitute
Simplify the equation to find
Therefore, the current function of the signal in Figure 1 is,
From the current expression
Conclusion:
Thus, the current equation is found and its respective waveform is drawn.
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