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In A.C. circuit the power curve is a sine wave having–
- a)Double the frequency of voltage
- b)Same frequency as that of voltage
- c)Half the frequency of the voltage
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In A.C. circuit the power curve is a sine wave havinga)Double the freq...
Understanding Power in A.C. Circuits
In an Alternating Current (A.C.) circuit, the relationship between voltage and power can be complex. One essential aspect is how the power waveform behaves in relation to the voltage waveform.
Frequency of Power vs. Voltage
- The power in an A.C. circuit is calculated using the formula:
- P(t) = V(t) * I(t)
- Here, V(t) is the voltage waveform and I(t) is the current waveform.
Voltage and Current Waveforms
- In a purely resistive circuit:
- Voltage (V) and current (I) are in phase, meaning they reach their maximum and minimum values simultaneously.
- In inductive or capacitive circuits:
- The current lags or leads the voltage, respectively.
Power Waveform Characteristics
- The product of two sinusoidal functions (voltage and current) produces a waveform that is not merely a sine wave.
- When you multiply two sine waves of the same frequency, the resulting waveform contains terms that double the frequency due to the trigonometric identity:
- sin(A) * sin(B) = 0.5 [cos(A-B) - cos(A+B)]
- Thus, the power waveform has components at twice the frequency of the original sine wave voltages and currents.
Conclusion
- Therefore, in A.C. circuits, the power curve indeed has a frequency that is double that of the voltage waveform, confirming that the correct answer is option 'A'.
This understanding is crucial for analyzing and designing A.C. electrical systems efficiently.
In an Alternating Current (A.C.) circuit, the relationship between voltage and power can be complex. One essential aspect is how the power waveform behaves in relation to the voltage waveform.
Frequency of Power vs. Voltage
- The power in an A.C. circuit is calculated using the formula:
- P(t) = V(t) * I(t)
- Here, V(t) is the voltage waveform and I(t) is the current waveform.
Voltage and Current Waveforms
- In a purely resistive circuit:
- Voltage (V) and current (I) are in phase, meaning they reach their maximum and minimum values simultaneously.
- In inductive or capacitive circuits:
- The current lags or leads the voltage, respectively.
Power Waveform Characteristics
- The product of two sinusoidal functions (voltage and current) produces a waveform that is not merely a sine wave.
- When you multiply two sine waves of the same frequency, the resulting waveform contains terms that double the frequency due to the trigonometric identity:
- sin(A) * sin(B) = 0.5 [cos(A-B) - cos(A+B)]
- Thus, the power waveform has components at twice the frequency of the original sine wave voltages and currents.
Conclusion
- Therefore, in A.C. circuits, the power curve indeed has a frequency that is double that of the voltage waveform, confirming that the correct answer is option 'A'.
This understanding is crucial for analyzing and designing A.C. electrical systems efficiently.
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