A power station generates (rms) and can supply up to of electrical power

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A power station generates

400\,\text{V}

(rms) and can supply up to

100\,\text{kW}

of electrical power. To transmit this power over overhead lines having a total resistance of

5\,\Omega

, an ideal step-up transformer raises the voltage to

20\,\text{kV}

before the lines, and an ideal step-down transformer at the receiving end restores it to

400\,\text{V}

for local distribution. Answer the following: (i) Calculate the turns ratio

\displaystyle \frac{N_s}{N_p}

of the step-up transformer. (ii) Determine the rms current in the transmission line when the power is transmitted at

20\,\text{kV}

. (iii) Compute the power dissipated as heat in the transmission line under these conditions. (iv) If the same

100\,\text{kW}

were transmitted directly at

400\,\text{V}

without transformers, find the rms line current and the corresponding power loss in the same

5\,\Omega

line. (v) Comment on the advantage of high-voltage transmission in the context of your numerical results.