Do the same exercise as above with the replacement of the earlier transformer by a 40,000-200 V step-down transformer (Neglect, as before, leakage losses though this may not be a good assumption any longer because of the very high voltage transmission involved). Hence, explain why high voltage transmission is preferred?

Solution

Given,

Primary voltage, V = 40000 V

Now, using the formula of power we get,
P = V_P I_P

\Rightarrow

40,000

\times I_{P}

= 800

\times 1000

I_P = 20 A
which, is the rms value of current or current in the primary coil.

(a) Line power loss = I_v² R
= (20)² × 15
= 6000 W
= 6 kW

(b) Power supplied by the plant = 800 + 6
= 806 kW

(c) Voltage drop on the line = I_P × R
= 20 × 15
= 300 V

$∴$ Voltage output of the step-up transformer at the plant = 40000 + 300= 40300 V

∴ The step-up transformer at the plant need a voltage of 440 V – 40300 V.

Power loss at lower voltage = $\frac{600}{1400} \times 100 = 43 %$

Power loss at higher voltage = $\frac{6}{800} \times 100 = 0.74 %$
Hence, it is evident that power loss is minimal when voltage is high. Therefore, high voltage transmission is produced.

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