Concept explainers
Use mesh analysis to find current io in the circuit of Fig. 10.74.
Figure 10.74
For Prob. 10.26.
Find the current
Answer to Problem 26P
The value of current
Explanation of Solution
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:
Comparing given source voltage
Substitute
Convert
Substitute
Substitute
The frequency domain representation of given figure with the assumed current direction is shown in Figure 1.
Apply Kirchhoff’s voltage law to the loop with current
Apply Kirchhoff’s voltage law to the loop with current
Represent equation (5) and (6) in matrix form.
Obtain the value of determinants as follows.
Write the expression for mesh currents using Cramer’s rule.
Substitute
Substitute
From Figure 1, write the expression for current
Substitute
Represent the current in time domain.
Conclusion:
Therefore, the value of current
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Chapter 10 Solutions
Fundamentals of Electric Circuits
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