(a) Determine a numerical value for each current and voltage (i1, v1, etc.) in the circuit of Fig. 3.64. (b) Calculate the power absorbed by each element and verify that they sum to zero.
FIGURE 3.64
(a)
Find the value of current and voltage in the circuit.
Answer to Problem 23E
The current
The voltage
Explanation of Solution
Calculation:
The redrawn circuit is shown in Figure 1
Refer to the Figure 1.
Since there is no voltage drop across branch
Here,
Refer to the Figure 1.
The expression for KCL at node
Here,
Refer to the Figure 1.
By ohm’s law the voltage across branch
Here,
Refer to the Figure 1
The expression for current
Refer to the Figure 1.
The expression for voltage
Here,
Refer to the Figure 1.
Since, the voltage across branch
Here,
By ohm’s law the voltage across branch is
The expression for KCL at node is
The expression for KVL across the loop
Refer to the Figure 1.
Substitute
Substitute
Rearrange for
Substitute
Substitute
Substitute
Substitute
Substitute
Rearrange for
Substitute
Rearrange for
Substitute
Rearrange for
Conclusion:
Thus, the current
The voltage
(b)
Calculate the power absorbed by each element and verify total sum of power absorbed is zero.
Answer to Problem 23E
The power absorbed by independent voltage source is
The power absorbed by
The power absorbed by dependent current source is
The power absorbed by dependent voltage source is
The power absorbed by
Explanation of Solution
Formula used:
Refer to the Figure 1.
The expression for power supply by the voltage source from branch
Here,
The expression for power absorbed by resistance
The expression for power supply by the current dependent source from branch
The expression for power supply by the voltage dependent source from branch
The expression for power dissipate by the resistance
The expression for sum of total power absorbed in the circuit is,
Calculation:
Refer to the Figure 1.
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
Thus, the power absorbed by independent voltage source is
The power absorbed by
The power absorbed by dependent current source is
The power absorbed by dependent voltage source is
The power absorbed by
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Chapter 3 Solutions
Engineering Circuit Analysis
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