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A 10 kVA, 400/200 V, 1-phase transformer with 2% resistance and 2% leakage reactance. It draws steady short circuit current at angle of
- a)45°
- b)75°
- c)135°
- d)0°
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A 10 kVA, 400/200 V, 1-phase transformer with 2% resistance and 2% lea...
Given Data:
- Transformer Rating: 10 kVA, 400/200 V, 1-phase
- Resistance (R): 2%
- Leakage Reactance (X): 2%
Steps to Calculate the Angle of Short-Circuit Current:
Determine the Impedance: The impedance ZZZ of the transformer can be calculated using the given percentage values for resistance and reactance:
Z=R+jXZ = R + jXZ=R+jX
where RRR and XXX are the resistance and reactance.
Given:
R=2% of Z (assuming Z as base impedance, Z = 100)R = 2\% \text{ of } Z \text{ (assuming Z as base impedance, Z = 100)}R=2% of Z (assuming Z as base impedance, Z = 100) X=2% of Z (assuming Z as base impedance, Z = 100)X = 2\% \text{ of } Z \text{ (assuming Z as base impedance, Z = 100)}X=2% of Z (assuming Z as base impedance, Z = 100)
Calculate the Impedance Angle: The impedance angle θ\thetaθ is determined by:
θ=tan−1(XR)\theta = \tan^{-1} \left(\frac{X}{R}\right)θ=tan−1(RX)
Substituting R=2R = 2R=2 and X=2X = 2X=2:
θ=tan−1(22)=tan−1(1)=45°\theta = \tan^{-1} \left(\frac{2}{2}\right) = \tan^{-1}(1) = 45°θ=tan−1(22)=tan−1(1)=45°
Angle of the Short-Circuit Current:
The angle of the short-circuit current is equal to the angle of the impedance because the current in a short-circuit condition is essentially the same as the impedance angle.
Conclusion:
The steady short-circuit current draws at an angle of:
1. 45°
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A 10 kVA, 400/200 V, 1-phase transformer with 2% resistance and 2% lea...
The angle at which the short circuit current is drawn can be determined using the impedance of the transformer.
The impedance of a transformer is given by the sum of its resistance and reactance.
The resistance is 2% of the transformer's apparent power, which is 10 kVA.
Resistance = 0.02 * 10 kVA = 200 VA
The reactance is also 2% of the transformer's apparent power.
Reactance = 0.02 * 10 kVA = 200 VA
The total impedance of the transformer is given by:
Impedance = √(Resistance² + Reactance²)
Impedance = √(200² + 200²) = √(40000 + 40000) = √80000 = 282.84 VA
The angle at which the short circuit current is drawn can be determined using the following formula:
Angle = arctan(Reactance / Resistance)
Angle = arctan(200 / 200) = arctan(1) = 45 degrees
Therefore, the steady short circuit current is drawn at an angle of 45 degrees.
The impedance of a transformer is given by the sum of its resistance and reactance.
The resistance is 2% of the transformer's apparent power, which is 10 kVA.
Resistance = 0.02 * 10 kVA = 200 VA
The reactance is also 2% of the transformer's apparent power.
Reactance = 0.02 * 10 kVA = 200 VA
The total impedance of the transformer is given by:
Impedance = √(Resistance² + Reactance²)
Impedance = √(200² + 200²) = √(40000 + 40000) = √80000 = 282.84 VA
The angle at which the short circuit current is drawn can be determined using the following formula:
Angle = arctan(Reactance / Resistance)
Angle = arctan(200 / 200) = arctan(1) = 45 degrees
Therefore, the steady short circuit current is drawn at an angle of 45 degrees.
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