Question

A thermal power plant produces electric power of $500kW$ at $2500V$. The electrical energy is transported $200km$ away for distribution at $240V$.
If the resistance of the transmission cable is $0.025\Omega /km$, how much will be the current in the distribution line?

• A. 1250 A
• B. 2500 A
• C. 625 A
• D. 1875 A

Answer 1

The correct option is A 1250 A

Given:
Power produced, $P_1=500kW$
Generating voltage, $V_1=2500V$
Resistance per unit length, $\alpha =0.025\Omega /km$
Length of transmission line, $L=200km$
Distribution voltage, $V_2=240V$

Let the current near the thermal power plant be $I_1$.
From definition of power,
$P_1=V_1{I}_1$
$5\times {10}^5=2500I_1$
$I_1=200A$

Total resistance of transmission cable:
$R=\alpha L$
$R=0.025\times 200=5\Omega$

Power loss during transmission,
$P_{loss}=I_1^2\times R$
$P_{loss}={200}^2\times 5=200kW$

Power reaching to the distribution transformer,
$P_2=P_1-P_{loss}$
$P_2=500-200=300kW$

Assuming ideal transformer and using definition of power,
$P_2=V_2\times I_2$
$3\times {10}^5=240I_2$
$I_2=1250A$