First slide

Thermal effect of current

Question

An electrical power line, having a total resistance of $2 Ω$ , delivers $1 k W a t 220 V$ . The efficiency of the transmission line is approximately.

Moderate

A

$72 %$
B

$85 %$
C

$96 %$
D

$91 %$

Solution

$\begin{array}{l} Current=i= \frac{P}{V} = \frac{1000}{220} A \\ \begin{array}{l} \Rightarrow power loss = {(\frac{1000}{220})}^{2} (2) \\ = \frac{10000}{242} W \\ E f f i c i e n c y = n = \frac{P_{o u t}}{P_{i n}} \times 100 \\ \Rightarrow n = \frac{P_{o u t}}{(P_{o u t} + P_{l o s s})} \times 100 \end{array} \\ \Rightarrow n = (\frac{10000}{10000 + \frac{10000}{242}}) \times 100 % = 99.6 % \approx 96 % (c l o s e s t o p t i o n) \end{array}$

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