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JIPMER 2016
Exam
JIPMER
Year
2016
Subject
Physics
Chapter
Current Electricity

JIPMER 2016 · Physics · Current Electricity

A rod made up of metal is 1.2 m long and 0.8 cm in diameter. Its...

A rod made up of metal is 1.2 m long and 0.8 cm in diameter. Its resistance is 3.5×10−3Ω3.5 \times 10^{-3} \Omega. Another disc made of the same metal is 2.0 cm in diameter and 1.25 mm thick. What is the resistance between the round faces of the disc?

Options

  1. A1.35×10−8Ω1.35 \times 10^{-8} \Omega
  2. B2.70×10−7Ω2.70 \times 10^{-7} \Omega
  3. C5.82×10−7Ω5.82 \times 10^{-7} \Omega
  4. D8.10×10−5Ω8.10 \times 10^{-5} \Omega

Correct answer

C. 5.82×10−7Ω5.82 \times 10^{-7} \Omega

Step-by-step solution

Given, I=12 m,d=0.8 cmI=12 \mathrm{~m}, d=0.8 \mathrm{~cm}, R=3.5×10−3ΩR=3.5 \times 10^{-3} \Omega, thickness =1.25 mm=1.25 \mathrm{~mm}, Resistivity of the material of the rod ρ=RAI=3.5×10−3×π(0.4×10−2)21.2=46.6×10−9πΩm\begin{aligned} \rho & =\frac{R A}{I}=\frac{3.5 \times 10^{-3} \times \pi\left(0.4 \times 10^{-2}\right)^2}{1.2} \\ & =46.6 \times 10^{-9} \pi \Omega \mathrm{m}\end{aligned} Resistance of disc, R=ρ (Thickness)  Area of cross-section =46.6×10−9π×(1.25×10−3)π(1×10−2)2=5.82×10−7Ω\begin{aligned} & \text{ Resistance of disc, } R=\frac{\rho \text{ (Thickness) }}{\text{ Area of cross-section }} \\ &= \frac{46.6 \times 10^{-9} \pi \times\left(1.25 \times 10^{-3}\right)}{\pi\left(1 \times 10^{-2}\right)^2} \\ &= 5.82 \times 10^{-7} \Omega\end{aligned}$
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