First slide

Resistivity of various materials

Question

Two solid conductors are made up of same material, have same length and same resistance. One of them has a circular cross section of area $A_{1}$ and the other one has asquare cross section of area $A_{2}$ . The ratio $A_{1} / A_{2}$ is

Very Easy

A

2
B

1.5
C

1
D

0.8

Solution

Resistance of conductoris given as
$\begin{aligned} \begin{matrix} R = \frac{ρl}{A} \\ ∴ A = \frac{ρl}{R} \\ \Rightarrow \frac{A_{1}}{A_{2}} = \frac{ρ_{1}}{ρ_{2}} \times \frac{l_{1}}{I_{2}} (\frac{R_{2}}{ℝ_{1}}) \end{matrix} \\ \Rightarrow \frac{A_{1}}{A_{2}} = 1 [∵ R_{1} = R_{2}, I_{1} = I_{2} and for same \\ material ρ_{1} = ρ_{2}] \end{aligned}$

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