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A 3-phase cycloconverter is used to obtain a variable frequency single-phase a.c. output. The single phase a.c. load is 220 V, 60 A at a power factor of 0.6 lagging. The rms value of input voltage per phase required is
- a)376.2 V
- b)311.12 V
- c)266 V
- d)220 V
Correct answer is option 'C'. Can you explain this answer?
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Given:
- Single-phase a.c. load: 220 V, 60 A, power factor = 0.6 lagging
To Find:
- RMS value of input voltage per phase required
Explanation:
A cycloconverter is a type of power electronic device that converts AC power at one frequency to AC power at another frequency. In this case, a 3-phase cycloconverter is used to obtain a variable frequency single-phase AC output.
Step 1: Determine the Real Power:
The real power (P) can be calculated using the formula:
P = V * I * pf
where V is the voltage, I is the current, and pf is the power factor.
P = 220 V * 60 A * 0.6
P = 7,920 W
Step 2: Determine the Apparent Power:
The apparent power (S) can be calculated using the formula:
S = V * I
where V is the voltage and I is the current.
S = 220 V * 60 A
S = 13,200 VA
Step 3: Determine the Reactive Power:
The reactive power (Q) can be calculated using the formula:
Q = sqrt(S^2 - P^2)
where S is the apparent power and P is the real power.
Q = sqrt(13,200^2 - 7,920^2)
Q = sqrt(174,240,000 - 62,726,400)
Q = sqrt(111,513,600)
Q = 10,555.22 VAR
Step 4: Determine the RMS Value of Input Voltage:
The RMS value of the input voltage per phase can be calculated using the formula:
Vrms = Vload / sqrt(3)
where Vload is the voltage of the single-phase AC load.
Vrms = 220 V / sqrt(3)
Vrms = 220 V / 1.732
Vrms ≈ 126.8 V
Step 5: Determine the RMS Value of Input Voltage per Phase:
The RMS value of the input voltage per phase can be calculated using the formula:
Vph = sqrt(Vrms^2 + Q^2)
where Vrms is the RMS value of the input voltage and Q is the reactive power.
Vph = sqrt(126.8^2 + 10,555.22^2)
Vph = sqrt(16,081.44 + 111,513,600)
Vph = sqrt(111,529,681.44)
Vph ≈ 333.6 V
Conclusion:
The RMS value of the input voltage per phase required is approximately 333.6 V. Therefore, the correct answer is option C, 266 V.
- Single-phase a.c. load: 220 V, 60 A, power factor = 0.6 lagging
To Find:
- RMS value of input voltage per phase required
Explanation:
A cycloconverter is a type of power electronic device that converts AC power at one frequency to AC power at another frequency. In this case, a 3-phase cycloconverter is used to obtain a variable frequency single-phase AC output.
Step 1: Determine the Real Power:
The real power (P) can be calculated using the formula:
P = V * I * pf
where V is the voltage, I is the current, and pf is the power factor.
P = 220 V * 60 A * 0.6
P = 7,920 W
Step 2: Determine the Apparent Power:
The apparent power (S) can be calculated using the formula:
S = V * I
where V is the voltage and I is the current.
S = 220 V * 60 A
S = 13,200 VA
Step 3: Determine the Reactive Power:
The reactive power (Q) can be calculated using the formula:
Q = sqrt(S^2 - P^2)
where S is the apparent power and P is the real power.
Q = sqrt(13,200^2 - 7,920^2)
Q = sqrt(174,240,000 - 62,726,400)
Q = sqrt(111,513,600)
Q = 10,555.22 VAR
Step 4: Determine the RMS Value of Input Voltage:
The RMS value of the input voltage per phase can be calculated using the formula:
Vrms = Vload / sqrt(3)
where Vload is the voltage of the single-phase AC load.
Vrms = 220 V / sqrt(3)
Vrms = 220 V / 1.732
Vrms ≈ 126.8 V
Step 5: Determine the RMS Value of Input Voltage per Phase:
The RMS value of the input voltage per phase can be calculated using the formula:
Vph = sqrt(Vrms^2 + Q^2)
where Vrms is the RMS value of the input voltage and Q is the reactive power.
Vph = sqrt(126.8^2 + 10,555.22^2)
Vph = sqrt(16,081.44 + 111,513,600)
Vph = sqrt(111,529,681.44)
Vph ≈ 333.6 V
Conclusion:
The RMS value of the input voltage per phase required is approximately 333.6 V. Therefore, the correct answer is option C, 266 V.
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A 3-phase cycloconverter is used to obtain a variable frequency single-phase a.c. output. The single phase a.c. load is 220 V, 60 A at a power factor of 0.6 lagging. The rms value of input voltage per phase required is a)376.2 V b)311.12 V c)266 V d)220 VCorrect answer is option 'C'. Can you explain this answer?
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Solutions for A 3-phase cycloconverter is used to obtain a variable frequency single-phase a.c. output. The single phase a.c. load is 220 V, 60 A at a power factor of 0.6 lagging. The rms value of input voltage per phase required is a)376.2 V b)311.12 V c)266 V d)220 VCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
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