Concept explainers
Compute the power absorbed by each element in the circuit of Fig. 3.68 if the mysterious element X is (a) a 13 Ω resistor; (b) a dependent voltage source labeled 4v1, “+” reference on top; (c) a dependent voltage source labeled 4ix, “+” reference on top.
FIGURE 3.68
(a)
Find the power absorbed by each element.
Answer to Problem 28E
Power absorbed by
Explanation of Solution
Given Data:
Element
Formula used:
The expression for power absorbed by voltage source is as follows.
Here,
The expression for power absorbed by resistor is as follows.
Here,
Calculation:
The circuit diagram is redrawn as shown in Figure 1.
Refer to the redrawn Figure 1.
The expression for KVL in mesh
Here,
Substitute
Rearrange equation (4) for
Current is leaving the positive terminal and we are calculating power absorbed hence current should leave by negative terminal so we will use magnitude of voltage with negative sign, therefore, value of
Substitute
So power absorbed by independent voltage source
Substitute
So, the power absorbed by resistor
Substitute
So power absorbed by resistor
Substitute
So power absorbed by resistor
Substitute
So power absorbed by independent voltage source
Substitute
So power absorbed by resistor
Conclusion:
Thus, power absorbed by
(b)
Find power absorbed by each element.
Answer to Problem 28E
Power absorbed by
Explanation of Solution
Given Data:
Element
Calculation:
The circuit diagram is redrawn as shown in Figure 2,
Refer to the redrawn Figure 2,
The expression for KVL in mesh
Here,
The expression for voltage
Here,
The expression for voltage
Here,
Refer to the redrawn Figure 2,
Substitute
Substitute
Rearrange equation (9) for
Current is leaving the positive terminal and we are calculating power absorbed hence current should leave by negative terminal so we will use magnitude of voltage with negative sign, therefore, value of
Substitute
So power absorbed by independent voltage source
Substitute
So power absorbed by resistor
Substitute
So power absorbed by resistor
Substitute
Substitute
Substitute
So power absorbed by dependent voltage source
Substitute
So power absorbed by independent voltage source
Substitute
So power absorbed by resistor
Conclusion:
Thus, power absorbed by
(c)
Find power absorbed by each element.
Answer to Problem 28E
Power absorbed by
Explanation of Solution
Given Data:
Element
Calculation:
The circuit diagram is redrawn as shown in Figure 3.
Refer to the redrawn Figure 3,
The expression for KVL in mesh
Here,
The expression for voltage
Here,
Refer to the redrawn Figure 2,
Substitute
Rearrange equation (12) for
Current is leaving the positive terminal and we are calculating power absorbed hence current should leave by negative terminal so we will use magnitude of voltage with negative sign, therefore, value of
Substitute
So power absorbed by independent voltage source
Substitute
So power absorbed by resistor
Substitute
So power absorbed by resistor
Substitute
Substitute
So power absorbed by dependent voltage source
Substitute
So power absorbed by independent voltage source
Substitute
So power absorbed by resistor
Conclusion:
Thus, power absorbed by
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