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)
Solution
${{{R_1}{R_2}} \over {{R_1} + {R_2}}} = 3$<br><br>$${{{{(12 \times {{10}^{ - 6}} \times {{10}^{ - 2}})} \over {\pi {{(2)}^2} \times {{10}^{ - 6}}}} \times {{(51 \times {{10}^{ - 6}} \times {{10}^{ - 2}})l \times 4} \over {\pi {{(2)}^2} \times {{10}^{ - 6}}}}} \over {{{63 \times {{10}^{ - 6}} \times {{10}^{ - 2}} \times l \times 4} \over {\pi {{(2)}^2} \times {{10}^{ - 6}}}}}}$$ = 3<br><br>$\Rightarrow$ l = 97 m
About this question
Subject: Physics · Chapter: Current Electricity · Topic: Kirchhoff's Laws
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