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A rod of a certain metal is 1.0 m long and 0.6 cm in diameter. Its resistance is $3.0 \times 10^{- 3} o h m .$ Another disc made of the same metal is 2.0 cm in diameter and 1.0 mm thick. What is the resistance between the round faces of the disc?

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$1.35 \times 10^{- 8} o h m$

$2.70 \times 10^{- 7} o h m$

$4.05 \times 10^{- 6} o h m$

$8.10 \times 10^{- 5} o h m$

answer is B.

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Detailed Solution

Resistivity of the material of the rod

$\begin{array}{l} 8.10 \times 10^{- 5} o h m \\ ρ = \frac{R A}{l} = \frac{3 \times 10^{- 3} π {(3 \times 10^{- 2})}^{2}}{1} = 27 \times 10^{- 9} π Ω m \end{array}$

Resistance of disc $R = ρ \frac{T h i c k n e s s}{A r e a o f c r o s s \sec t i o n}$

$= 27 \times 10^{- 19} π \times \frac{(10^{- 3})}{π \times {(1 \times 10^{- 2})}^{2}} = 2.7 \times 10^{- 7} Ω$

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