Question

An autotransformer is required to step-up a voltage from 220 volts to 250 volts. The total number of coil turns on the transformer main winding is 2000. Determine the position of the primary tapping point (turns associated with the primary side). Also, find the primary and secondary currents when the output is rated at 10 kVA and the efficiency.

a) Primary tapping point: 250 turns, Primary current: 45.45 A, Secondary current: 40 A, Efficiency: 88.89%
b) Primary tapping point: 280 turns, Primary current: 50 A, Secondary current: 36 A, Efficiency: 92.85%
c) Primary tapping point: 240 turns, Primary current: 48.19 A, Secondary current: 44 A, Efficiency: 85.62%
d) Primary tapping point: 260 turns, Primary current: 47.83 A, Secondary current: 42 A, Efficiency: 90.71%

Answer 1

The primary tapping point for the autotransformer with a total of 2000 turns is at 1760 turns. The primary current is 45.45 A, and the secondary current is 40 A. Efficiency cannot be calculated without information about the losses.

Step-by-step explanation:

To calculate the primary tapping point for an autotransformer required to step-up a voltage from 220 volts to 250 volts with a total of 2000 coil turns, we use the following formula derived from the transformer equation:

Vp/Vs = Np/Ns

Where:

• Vp is the primary voltage (220V)
• Vs is the secondary voltage (250V)
• Np is the number of primary turns (what we are looking for)
• Ns is the number of secondary turns (2000)

Solving for Np, we find:

Np = (Vp × Ns) / Vs

Np = (220 × 2000) / 250 = 1760 turns

To find the primary current (Ip), we use the power formula:

S = Vs × Is

Where S is the apparent power rated at 10kVA (10,000VA), we know the secondary current is:

Is = S / Vs = 10,000 / 250 = 40 A

Because power is conserved in a transformer, Sp = Ss, and:

Ip = S / Vp = 10,000 / 220 = 45.45 A

The efficiency can be calculated if losses are known, which are not provided in this question. Therefore, the efficiency cannot be determined from the given data.