Atransmission line that has a resistance per unit length of 2.40 10-4 ω/m is to be used to transmit 5.00 mw across 400 mi (6.44 105 m). the output voltage of the source is 4.50 kv. (a) what is the line loss if a transformer is used to step up the voltage to 506 kv? (b) what fraction of the input power is lost to the line under these circumstances? (c) what difficulties would be encountered in attempting to transmit the 5.00 mw at the source voltage of 4.50 kv?

(a) 30.174 kW

(b)

(c) I = 1.112 kA

Solution:

As per the question:

Resistance per unit length,

Power transmitted, P = 5.00 MW =

Length, L =

Output voltage, V = 4.50 kV

Stepped-up Voltage, V' = 506 kV

Now,

(a) The line loss can be calculated as:

Current, I =

To calculate the power loss:

where

R = Resistance in the transmission line

R =

Thus

(b) Fraction of the input power lost is given by:

(c) To calculate the current at the sending end at ther source voltage of 4.50 kV:

This value of current is very high and sending such a high watt power is impossible, even if the circuit at the other end is open then also this current can be destructive.

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