A generator produces 20A (rms) of current at 800 V. The voltage is stepped up to

Question

A generator produces 20A (rms) of current at 800 V. The voltage is stepped up to 9000 V by an ideal transformer and transmitted a long distance through a power line of total resistance 60 ohms.

(A) Determine the current in the transmission line.

(B) Calculate the power lost in the transmission line.

(C) What is the ratio of power lost before, and after the voltage is stepped up (I am asking for the percentage of power loss when voltage is stepped up)?

(D) What percentage of the original power would be lost in the transmission line if the voltage were not stepped up?

Explanation / Answer

A)

ip = primary current = 20 A

Vp = primary voltage = 800 Volts

is = secondary current = ?

Vs = secondary voltage = 9000 Volts

using the formula

Vsis = Vpip

9000 is = 800 x 20

is = 1.8 A

B)

power lost is given as

Plost = i2s R = (1.8)2 (60) = 216 watt

c)

P'lost = power lost before = i2p R = (20)2 (60) = 24000 watt

%age = Plost x 100 /P'lost = 216 x 100/24000= 0.9 %

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