Concept explainers
Solve for vo(t) in the circuit of Fig. 10.91 using the superposition principle.
Figure 10.91
Calculate the voltage
Answer to Problem 46P
The value of voltage
Explanation of Solution
Given data:
Refer to Figure 10.91 in the textbook.
Formula used:
Write the expression to calculate impedance of the inductor.
Here,
Write the expression to calculate impedance of the capacitor.
Here,
Write the general representation of sinusoidal cosine function.
Here,
Write the general expression to phasor transform of sinusoidal function from time domain to frequency domain.
Here,
Write the polar form representation of frequency domain.
Write the general representation of sinusoidal sine function.
Here,
Write the general expression to phasor transform of sinusoidal function from time domain to frequency domain.
Here,
Write the polar form representation of frequency domain.
Calculation:
Let
Consider that
The capacitor acts like an open circuit for DC source. Therefore, the entire source voltage will appear across the capacitor.
Consider that
Comparing
Substitute
Substitute
Substitute
The frequency domain representation of figure 2 is shown in Figure 3.
In Figure 3, the reduce the parallel combination of
The reduced circuit is shown in Figure 4.
From Figure 4, calculate the current flows through the capacitor using current division rule.
Write the expression to calculate the voltage
Substitute
Write the time domain representation of voltage
Consider that
Comparing
Substitute
Substitute
Substitute
The frequency domain representation of figure 5 is shown in Figure 6.
Apply Kirchhoff’s current law at node
Simplify the equation as follows.
Write the time domain representation of voltage
Write the expression for
Substitute
Conclusion:
Thus, the value of voltage
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