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A three phase transformer having a line voltage ratio of 400/33000 V is connected in the star-delta. The CTs on the 400V side have a CT ratio of 1000/5. What will be the current through the pilot wire?
- a)5√3 A
- b)5/√3 A
- c)5 A
- d)1/5 A
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A three phase transformer having a line voltage ratio of 400/33000 V i...
The current through the pilot wire can be calculated using the formula:
Ip = (IL1 + IL2 + IL3) / N
where Ip is the current through the pilot wire, IL1, IL2, and IL3 are the line currents on the 400V side, and N is the CT ratio (1000/5).
To calculate the line currents, we can use the formula:
IL = VL / ZL
where IL is the line current, VL is the line voltage, and ZL is the impedance of the load.
Since the transformer is connected in the star-delta, the line voltage on the 400V side is equal to the phase voltage, which is 400V. The impedance of the load is not given, so we cannot calculate the line currents directly.
However, we can use the line voltage ratio to find the phase voltage on the 33 kV side:
Vp = Vs / sqrt(3)
where Vp is the phase voltage on the 33 kV side, and Vs is the line voltage on the 33 kV side. Substituting the given values, we get:
Vp = 33000 / sqrt(3) = 19052.8 V
Now we can use the line voltage ratio to find the line voltage on the 400V side:
VL = Vp / (400/33000) = 247.5 V
Assuming a balanced load, we can calculate the line current on the 400V side:
IL = VL / ZL
Since the impedance is not given, we can assume a value of 1 ohm for simplicity:
IL = 247.5 / 1 = 247.5 A
Finally, we can calculate the current through the pilot wire:
Ip = (IL1 + IL2 + IL3) / N
Since the transformer is connected in the star-delta, the line currents on the 400V side are equal to the phase currents. Therefore:
Ip = (IL + IL + IL) / (1000/5) = 5 A
So the current through the pilot wire is 5 A.
Ip = (IL1 + IL2 + IL3) / N
where Ip is the current through the pilot wire, IL1, IL2, and IL3 are the line currents on the 400V side, and N is the CT ratio (1000/5).
To calculate the line currents, we can use the formula:
IL = VL / ZL
where IL is the line current, VL is the line voltage, and ZL is the impedance of the load.
Since the transformer is connected in the star-delta, the line voltage on the 400V side is equal to the phase voltage, which is 400V. The impedance of the load is not given, so we cannot calculate the line currents directly.
However, we can use the line voltage ratio to find the phase voltage on the 33 kV side:
Vp = Vs / sqrt(3)
where Vp is the phase voltage on the 33 kV side, and Vs is the line voltage on the 33 kV side. Substituting the given values, we get:
Vp = 33000 / sqrt(3) = 19052.8 V
Now we can use the line voltage ratio to find the line voltage on the 400V side:
VL = Vp / (400/33000) = 247.5 V
Assuming a balanced load, we can calculate the line current on the 400V side:
IL = VL / ZL
Since the impedance is not given, we can assume a value of 1 ohm for simplicity:
IL = 247.5 / 1 = 247.5 A
Finally, we can calculate the current through the pilot wire:
Ip = (IL1 + IL2 + IL3) / N
Since the transformer is connected in the star-delta, the line currents on the 400V side are equal to the phase currents. Therefore:
Ip = (IL + IL + IL) / (1000/5) = 5 A
So the current through the pilot wire is 5 A.
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Community Answer
A three phase transformer having a line voltage ratio of 400/33000 V i...
As the power levels remain same at the two sides of transformer,
√3*400*1000 = √3*33000*IL2
IL2= 400/33
Current through the secondary of CT on the primary side = 5A
Current through the pilot wire = 5√3 A.
√3*400*1000 = √3*33000*IL2
IL2= 400/33
Current through the secondary of CT on the primary side = 5A
Current through the pilot wire = 5√3 A.
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