JEE MAIN - Physics (2021 - 26th August Morning Shift - No. 16)
What equal length of an iron wire and a copper-nickel alloy wire, each of 2 mm diameter connected parallel to give an equivalent resistance of 3$$\Omega$$ ?
(Given resistivities of iron and copper-nickel alloy wire are 12 $$\mu$$$$\Omega$$ and 51 $$\mu$$$$\Omega$$ cm respectively)
(Given resistivities of iron and copper-nickel alloy wire are 12 $$\mu$$$$\Omega$$ and 51 $$\mu$$$$\Omega$$ cm respectively)
82 m
97 m
110 m
90 m
Explanation
$${{{R_1}{R_2}} \over {{R_1} + {R_2}}} = 3$$
$${{{{(12 \times {{10}^{ - 6}} \times {{10}^{ - 2}})} \over {\pi {{(2)}^2} \times {{10}^{ - 6}}}} \times {{(51 \times {{10}^{ - 6}} \times {{10}^{ - 2}})l \times 4} \over {\pi {{(2)}^2} \times {{10}^{ - 6}}}}} \over {{{63 \times {{10}^{ - 6}} \times {{10}^{ - 2}} \times l \times 4} \over {\pi {{(2)}^2} \times {{10}^{ - 6}}}}}}$$ = 3
$$\Rightarrow$$ l = 97 m
$${{{{(12 \times {{10}^{ - 6}} \times {{10}^{ - 2}})} \over {\pi {{(2)}^2} \times {{10}^{ - 6}}}} \times {{(51 \times {{10}^{ - 6}} \times {{10}^{ - 2}})l \times 4} \over {\pi {{(2)}^2} \times {{10}^{ - 6}}}}} \over {{{63 \times {{10}^{ - 6}} \times {{10}^{ - 2}} \times l \times 4} \over {\pi {{(2)}^2} \times {{10}^{ - 6}}}}}}$$ = 3
$$\Rightarrow$$ l = 97 m
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