A pair of power transmission lines each have 2.35-Ω resistance and carry 650 Amp. If the primary voltage of the 10:1 step-up transformer is 3.0 kV, calculate the input voltage of the step-down transformer at the other end.

The input voltage of the step-down transformer is 26.945 kV

Explanation:

Given:

R = 2.35 Ω

I = 650 A

Vs = 10 V

Vp = 1 V

Vs/Vp = 10/1 = 10

Vp = 3 kV

Vs = 10*Vp = 3*10 = 30 kV

The input voltage of the step-down is:

V = Vs - 2IR = 30000 - (2 * 650 * 2.35) = 26945 V = 26.945 kV

Given that

R = 2 Ω

I = 650 A

Step Up Transformer =

Vs = 10 V, Vp = 1 V

Vs / Vp = 10 / 1

as Vp = 2.6 KV

so,

Vs = Vp * 10 = 2.6 * 10 = 26 KV

Input Voltage of the step down transformer

V = Vs - 2 IR

V = (26 * 10^3) - (2 * 650 * 2) note; here we convert KV into V by

multiplying KV amount to 1000.

Input voltage of the step-down transformer

V = Vs - 2 IR

V = (26 * 10^3) - (2 * 650 * 2)

V = 23400 V

V = 23.4 KV