Concept explainers
For each of the following cases, find the complex power, the average power, and the reactive power:
- (a) v(t) = 169.7 sin (377t + 45°) V,
i(t) = 5.657 sin (377t) A
- (b) v(t) = 339.4 sin (377t + 90°) V,
i(t) = 5.657 sin (377t + 45°) A
(a)
Find the complex power, average power, and reactive power for the given instantaneous voltage and current.
Answer to Problem 47P
The complex power is
Explanation of Solution
Given data:
The voltage phasor is,
The current phasor is,
Formula used:
Write the expression to find the complex power
Here,
Write the expression for complex power
Here,
Calculation:
From equation (1), the rms value of the voltage is
From equation (2), the rms value of the current is
Substitute
Convert equation (5) from polar form to rectangular form. Therefore,
On comparing equation (4) and (6), the average power
Conclusion:
Thus, the complex power is
(b)
Find the complex power, average power, and reactive power for the given instantaneous voltage and current.
Answer to Problem 47P
The complex power is
Explanation of Solution
Given data:
The voltage phasor,
The current phasor,
Calculation:
From equation (7), the rms value of the voltage is
From equation (8), the rms value of the current is
Substitute
Convert equation (9) from polar form to rectangular form. Therefore,
On comparing equation (4) and (10), the average power
Conclusion:
Thus, the complex power is
(c)
Find the complex power, average power, and reactive power for the given voltage and impedance phasor.
Answer to Problem 47P
The complex power is
Explanation of Solution
Given data:
The voltage phasor,
The impedance phasor,
Formula used:
Write the expression for complex power
Here,
Calculation:
From equation (11),
Substitute
Convert equation (14) from polar form to rectangular form. Therefore,
On comparing equation (4) and (15), the average power
Conclusion:
Thus, the complex power is
(d)
Find the complex power, average power, and reactive power for the given voltage and impedance phasor.
Answer to Problem 47P
The complex power is
Explanation of Solution
Given data:
The current phasor,
The impedance phasor,
Write the expression to find the complex power
Calculation:
From equation (16),
Substitute
Convert equation (19) from polar form to rectangular form. Therefore,
On comparing equation (4) and (20), the average power
Conclusion:
Thus, the complex power is
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Chapter 11 Solutions
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