(a) Employ mesh analysis to determine the power dissipated by the 1 Ω resistor in the circuit represented schematically by Fig. 4.68. (b) Check your answer using nodal analysis.
■ FIGURE 4.68
(a)
Employ mess analysis to find the power dissipated by the
Answer to Problem 41E
The power dissipated by the
Explanation of Solution
Calculation:
The circuit diagram is redrawn as shown in Figure 1,
Refer to the redrawn Figure 1,
Apply KVL in the mesh
Here,
The expression for the current flowing in the branch
Here,
The expression for the current flowing in the branch
Here,
The expression for the power dissipated by the
Here,
Refer to the redrawn Figure 1,
Substitute
Rearrange equation (5),
Substitute
Substitute
Substitute
Rearrange the above equation for
Substitute
Rearrange for
Substitute
Substitute
Conclusion:
Thus, the power dissipated by the
(b)
Check the answer by nodal analysis.
Explanation of Solution
Formula used:
Refer to the redrawn Figure 1,
Apply KCL at node
Here,
Apply KCL at node
Here,
The expression for the current flowing in the branch
Apply KCL at node
Here,
The expression for the power dissipated by the
Here,
Calculation:
Refer to the redrawn Figure 1,
Substitute
Substitute
Substitute
Substitute
Substitute
Rearrange equation (13), (14) and (15),
The equations so formed can be written in matrix form as,
Therefore, by Cramer’s rule,
The determinant of the coefficient matrix is as follows,
The 1st determinant is as follows,
The 2nd determinant is as follows,
The 3rd determinant is as follows,
Simplify for
Simplify for
Simplify for
Substitute
So, the power dissipated by the
Conclusion:
Thus, the answer is checked by using nodal analysis.
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Chapter 4 Solutions
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