JEE MAIN - Physics (2020 - 5th September Morning Slot - No. 22)
An electrical power line, having a total
resistance of 2 $$\Omega $$, delivers 1 kW at 220 V. The
efficiency of the transmission line is
approximately :
85%
96%
72%
91%
Explanation
We know, $$\eta = {{{P_{out}}} \over {\left( {{P_{out}} + {P_{loss}}} \right)}} \times 100$$
Given, P= $$vi = {10^3}$$
$$ \therefore $$ $$i = {{1000} \over {220}}$$ = $${{50} \over {11}}$$ A
Power $$loss = {i^2}R = {\left( {{{50} \over {11}}} \right)^2} \times 2$$
$$ \therefore $$ efficiency $$ = {{1000} \over {1000 + {i^2}R}} \times 100 = 96\% $$
Given, P= $$vi = {10^3}$$
$$ \therefore $$ $$i = {{1000} \over {220}}$$ = $${{50} \over {11}}$$ A
Power $$loss = {i^2}R = {\left( {{{50} \over {11}}} \right)^2} \times 2$$
$$ \therefore $$ efficiency $$ = {{1000} \over {1000 + {i^2}R}} \times 100 = 96\% $$
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