An electrical power line, having a total resistance of 2 Ω, delivers 1 kW at 220 V. The efficiency of the transmission line is approximately :
Question
An electrical power line, having a total resistance of 2 Ω, delivers 1 kW at 220 V. The efficiency of the transmission line is approximately :
Solution
To find the efficiency of the transmission line, we first need to calculate the power loss in the transmission line and then subtract it from the total power to get the actual power delivered.
Step 1: Calculate the current in the line The power P delivered by the line is given by P = VI, where V is the voltage and I is the current. So we can solve for I:
I = P/V = 1000W/220V = 4.55 A
Step 2: Calculate the power loss in the line The power loss in the line is given by P_loss = I^2R, where R is the resistance of the line. So:
P_loss = (4.55 A)^2 * 2 Ω = 41.4 W
Step 3: Calculate the efficiency of the line The efficiency η of the line is given by η = (P - P_loss) / P
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