A rod made up of metal is 1.2 m long and 0.8 cm in diameter. Its resistance is 3.5 x 10^-3 Ω. 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?

1.35x 10^-8 Ω

2.70 x 10^-7 Ω

5.82 × 10^-7 Ω

8.10 × 10^-5 Ω

Solution

5.82 × 10^-7 Ω

Given:-

l = 12 m,

d = 0.8 cm,

R = 3.5 x 10^-3 Ω ,

thickness= 1.25 mm = 1.25 × 10^-3 m

Resistivity of the material of the rod

$ρ = \frac{R A}{l}$

= $\frac{3.5 \times 10^{- 3} \times π {(0.4 \times 10^{- 2})}^{2}}{1.2}$

= 46.6 × 10^-9 $π$ Ω m

Resistance of disc

R = $\frac{ρ (Thickness)}{Area of cross - section}$

= $\frac{46.6 \times 10^{- 9} π \times (1.25 \times 10^{- 3})}{π {(1 \times 10^{- 2})}^{2}}$

= 5.82 × 10^-7Ω

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