Concept explainers
Apply nodal analysis to find io and the power dissipated in each resistor in the circuit of Fig. 3.64.
Figure 3.64
For Prob. 3.15.
Find the current
Answer to Problem 15P
The value of current
Explanation of Solution
Given data:
Refer to Figure 3.64 in the textbook for the nodal analysis. In the given circuit,
Calculation:
Modify the given figure with the representation of supernode and current direction as shown in Figure 1.
Apply Kirchhoff’s current law to the supernode in Figure 1.
Apply Kirchhoff’s current law to node
Reduce the given figure to provide voltage relation as shown in Figure 2.
Apply Kirchhoff’s voltage law to the circuit in Figure 2 to get relationship between voltages.
Represent the equations (1), (2), and (3) in matrix form.
Obtain the value of determinants as follows.
Write the expression for the voltages
Substitute
Substitute
Substitute
From Figure 1, write the expression for the current
Substitute
Write the expression for power dissipated in
Substitute
Write the expression for power dissipated in
Substitute
Write the expression for power dissipated in
Substitute
Conclusion:
Therefore, the value of current
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Chapter 3 Solutions
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