Concept explainers
Using Fig. 10.61, design a problem to help other students better understand nodal analysis.
Figure 10.61
For Prob. 10.12.
Design a problem to provide better understanding of nodal analysis.
Explanation of Solution
Given data:
Refer to Figure 10.61 in the textbook for nodal analysis.
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 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:
In Figure 10.61, consider the value of source current
Comparing assumed source current with equation (3), the magnitude, angular frequency, and phase angle of source current are
Substitute
Substitute
Substitute
The frequency domain representation of given figure for assumed values is shown in Figure 1.
Apply Kirchhoff’s current law at node
From Figure 1, write the expression for current
Substitute equation (6) in (5).
Apply Kirchhoff’s current law at node
Substitute equation (6) in (8).
Rearrange equation (7).
Substitute equation (7) in (9).
Simplify the equation as follows.
Substitute
Represent the current in time domain.
Conclusion:
Thus, a problem has been designed to provide better understanding of nodal analysis.
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Chapter 10 Solutions
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