Concept explainers
(a)
The peak value of the current and average power delivered when a sinusoidal voltage of 40.0 V rms and a frequency of 100 Hz is applied to a 100 O resistor.
Answer to Problem 64QAP
When a sinusoidal voltage of 40.0 V rms and a frequency of 100 Hz is applied to a 100 O resistor, the peak current is found to be 0.57 A and the average power delivered is 16 W.
Explanation of Solution
Given:
Formula used:
The peak value of current
Here, the rms value of current
The average power dissipated in the circuit is given by,
Calculation:
Calculate the rms value of current
Calculate the value of peak current using equation (1).
Calculate the average power delivered using equation (3).
Conclusion;Thus, when a sinusoidal voltage of 40.0 V rms and a frequency of 100 Hz is applied to a 100 O resistor, the peak current is found to be 0.57 A and the average power delivered is 16 W.
(b)
The peak value of the current and average power delivered when a sinusoidal voltage of 40.0 V rms and a frequency of 100 Hz is applied to a 0.200 H inductor.
Answer to Problem 64QAP
When a sinusoidal voltage of 40.0 V rms and a frequency of 100 Hz is applied to a 0.200 H inductor, the peak current is found to be 0.45A and the average power delivered is 0 W.
Explanation of Solution
Given:
Formula used:
The peak value of current
Here, the rms value of current
The average power dissipated in the circuit is given by,
Here,
Calculation:
Calculate the rms value of current
Calculate the value of peak current using equation (1).
Calculate the average power delivered using equation (5). The phase difference between voltage and current in a ac circuit containing an inductor is 90o
Therefore, since
Conclusion;Thus, when a sinusoidal voltage of 40.0 V rms and a frequency of 100 Hz is applied to a 0.200 H inductor, the peak current is found to be 0.45A and the average power delivered is 0 W.
(c)
The peak value of the current and average power delivered when a sinusoidal voltage of 40.0 V rms and a frequency of 100 Hz is applied to a 50.0 μF capacitor.
Answer to Problem 64QAP
When a sinusoidal voltage of 40.0 V rms and a frequency of 100 Hz is applied to a 50.0 μF capacitor, the peak current is found to be 1.8 A and the average power delivered is 0 W.
Explanation of Solution
Given:
Formula used:
The peak value of current
Here, the rms value of current
The average power dissipated in the circuit is given by,
Here,
Calculation:
Calculate the rms value of current
Calculate the value of peak current using equation (1).
Calculate the average power delivered using equation (5). The phase difference between voltage and current in a ac circuit containing a capacitor is 90o
Therefore, since
Conclusion;Thus, when a sinusoidal voltage of 40.0 V rms and a frequency of 100 Hz is applied to a 50.0 μF capacitor, the peak current is found to be 1.8 A and the average power delivered is 0 W.
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Chapter 21 Solutions
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