Concept explainers
Use the superposition principle to obtain vx in the circuit of Fig. 10.89. Let vs = 50 sin 2t V and is = 12 cos(6t + 10°) A.
Figure 10.89
Calculate the voltage
Answer to Problem 44P
The value of voltage
Explanation of Solution
Given data:
Refer to Figure 10.89 in the textbook.
Formula used:
Write the expression to calculate impedance of the capacitor.
Here,
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.
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.
Calculation:
Let
Comparing
Substitute
Substitute
To find
In Figure 1, apply Kirchhoff’s current law at node
Simplify the above equation as follows.
Represent the voltage
Comparing
Substitute
Substitute
To find
In Figure 2, reduce the parallel combination of
The reduced circuit is as shown in Figure 3.
From Figure 3, write the expression for voltage
Represent the voltage
Write the expression for current
Substitute
Conclusion:
Thus, the value of voltage
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