A transformer is used to increase the voltage before power is transmitted along

Question

A transformer is used to increase the voltage before power is transmitted along long-distance electrical wires from the power plant to your home.

1. The power plant produces power with a voltage of 9970 V, and the power is transmitted through the power lines at a voltage of 269 000 V. If the primary coil has 912 turns, how many turns must the secondary coil have in order to increase the voltage that is supplied to the wires?

2. An average household in Sydney uses 16.3 kWh per day of electricity. There are currently 1 720 333 households in Sydney. What is the average power used by Sydney dwellings?

3.

If this power is transmitted through high voltage cables at a voltage of 269000 V, what current must flow along the wires?

Note: Ignore the power loss for this part

4. To keep the power loss below 0.5%, what is the maximum resistance the high voltage wires could have?

Explanation / Answer

1) N2/N1 = V2/V1

N2 / 912 = 269000/ 9970

N2 = 24606.6

so number of turns required = 24607

2) total power consumed = 1720333*16.3 *3.6*10^6 / 24*60*60 = 1.16*10^9 W ( 1kWh = 3.6*10^6 J)

3) P = VI

I = P/V = 1.16*10^9 / 269000 = 4343.46 A

4) Power lost = 0.5/100 * 1.16*10^9 = V^2 /R

R = 269000^2 * 100 / 0.5*1.16*10^9

= 12476 Ohm

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