Concept explainers
Although drawn so that it may not appear obvious at first glance, the circuit of Fig. 3.74 is in fact a single-node-pair circuit, (a) Determine the power absorbed by each resistor, (b) Determine the power supplied by each current source, (c) Show that the sum of the absorbed power calculated in (a) is equal to the sum of the supplied power calculated in (b).
FIGURE 3.74
(a)
Find power absorbed by each resistor.
Answer to Problem 34E
Power absorbed by the resistor
Explanation of Solution
Calculation:
The circuit diagram is redrawn as shown in Figure 1.
Refer to the redrawn Figure 1.
The expression for KCL at node
Here,
The expression for power absorbed by resistor is as follows.
Here,
Refer to the redrawn Figure 1.
Substitute
Rearrange equation (3) for
Substitute
Simplify for
So, power absorbed by resistor
Substitute
Simplify for
So, the power absorbed by resistor
Substitute
So, the power absorbed by resistor
Conclusion:
Thus, the power absorbed by resistor
(b)
Find the power supplied by each current source.
Answer to Problem 34E
Power supplied by dependent current source
Explanation of Solution
Formula used:
The expression for power supplied by current source is as follows.
Here,
Calculation:
Refer to the redrawn Figure 1.
As current direction for independent current source
Substitute
So power supplied by dependent current source
Substitute
So power supplied by dependent current source
Conclusion:
Thus, the power supplied by dependent current source
(c)
Verify that sum of power absorbed and sum of power supplied in the circuit is same.
Answer to Problem 34E
Sum of power absorbed and sum of power supplied in the circuit is same.
Explanation of Solution
Formula used:
The expression for power is as follows.
Here,
Calculation:
Substitute
So, the total power absorbed is
Substitute
So total power supplied is
Conclusion:
Thus, sum of power absorbed and sum of power supplied in the circuit is same.
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Chapter 3 Solutions
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