First slide

Electrical power

Question

An electric cable having a resistance of 0.4 $Ω$ delivers 10 kW at 200 v dc to a factory. The efficiency of transmission is

Moderate

A

65%
B

75%
C

80%
D

91%

Solution

Power loss in the cable $= i^{2} R = (P / V)^{2} R$
$= {(\frac{10000}{200})}^{2} \times 0 \cdot 4 = 1000 W = 1 kW$
$η = \frac{Power delivered by the cable to factory}{Power supplied to the cable}$
$= \frac{10}{10 + 1} = \frac{10}{11} = 0 \cdot 909 \approx 91 %$

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