A 676kW power station delivers power to a factory. The power is delivered throug

Question

A 676kW power station delivers power to a factory. The power is delivered through wires with a total (i.e. round-trip) resistance of 3.76Ohm. How much less power is wasted in the transmission wires if the electricity is delivered from the power station at 54200V rather than 13700V? (Hint: Consider the power plant as a battery delivering the voltage for the transmission line. How much current is flowing through the wire?) A 676kW power station delivers power to a factory. The power is delivered through wires with a total (i.e. round-trip) resistance of 3.76Ohm. How much less power is wasted in the transmission wires if the electricity is delivered from the power station at 54200V rather than 13700V? (Hint: Consider the power plant as a battery delivering the voltage for the transmission line. How much current is flowing through the wire?)

Explanation / Answer

we have P=VI

so in 1st case 676*10^3= 54200*I

so I= 12.4723 A

so power lost in wire= I^2*R

(12.4723)^2*3.76=584.9 W

if voltage is 13700 V

then current is

676000/13700=49.343 A

so power loss in wire= I^2*R=(49.343)^2*3.76 =9154.6 W

so difference in poweer wasted= 9154.6-584.9

= 8569.7 W

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