Verified Solution • 2025–26 Session moderate

QJEEM21Phdf7c: JEE Main 2021 Physics - Class 12 JEEM21Phdf7c Solution: What equal length of an iron wire and a copper-nickel alloy…

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 Ω\Omega ?

(Given resistivities of iron and copper-nickel alloy wire are 12 μ\mu Ω\Omega and 51 μ\mu Ω\Omega cm respectively)

Multiple Choice Options

  • A 82 m
  • B 97 m
  • C 110 m
  • D 90 m

Step-by-Step Verified Solution

R1R2R1+R2=3{{{R_1}{R_2}} \over {{R_1} + {R_2}}} = 3

(12×10−6×10−2)π(2)2×10−6×(51×10−6×10−2)l×4π(2)2×10−663×10−6×10−2×l×4π(2)2×10−6{{{{(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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