Do the same exercise as above with the replacement of the earlier transformer by a 40,000-220 V step-down transformer (Neglect, as before, leakage losses though this may not be a good assumption any longer because of the very high voltage transmission involved). Hence, explain why high voltage transmission is preferred?

The rating of a step-down transformer is 40000 V-220 V.
Input voltage,V, = 40000 V
Output voltage,V₂ = 220 V
Total electric power required,
P = 800 kW = 800 x 10³ W
Source potential, V = 220 V
Voltage at which the electric plant generates power,
V’ = 440 V
Distance between the town and power generating station, d = 15 km
Resistance of the two wire lines carrying power =0.5 Ω/km Total resistance of the wire lines,

R = (15 + 15)0.5 = 15 Ω

P= V1I

Rms current in the wire line is given as:

=> I = P/V1

= 800 x 10³/40000= 20 A

Ans (a).

Line power loss = I²R = (20)² x 15 = 6 kW

Ans (b).

Assuming that the power loss is negligible due to the leakage of current.

Hence, power supplied by the plant = 800 kW + 6kW = 806 kW

Ans (c).

Voltage drop in the power line = IR = 20 x 15 = 300 V

Hence, voltage that is transmitted by the power plant

= 300 + 40000 = 40300 V

The power is being generated in the plant at 440 V.

Hence, the rating of the step-up transformer needed at the plant is 440 V – 40300 V.

Hence, power loss during transmission

= (600/1400 )x 100 = 42.8%

1400

In the previous exercise, the power loss due to the same reason is (6/806 )x 100 = 0.744%

Since the power loss is less for a high voltage transmission, high voltage transmissions are preferred for this purpose.