Question

15) All (U), (l) and (II) (14) Only (III)
Two different wires, whose specific resistance are in
the ratio 2 : 3, length 3 : 4 and radius of cross-
section 1: 2. The ratio of their resistances is
(1) 3:4
(2) 16:9
(3) 5:6
(4) 2:1
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Answer 1

Answer:

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Answer 2

Answer:

Option (4) 2 : 1

Explanation:

If specific resistance is $\rho$ then Resistance of a wire of length $l$ and cross sectional area A is given by

$\boxed{R=\rho \frac{l}{A}}$

Given

$\frac{\rho_1}{\rho_2}=\frac{2}{3}$

$\frac{l_1}{l_2}=\frac{3}{4}$

$\frac{r_1}{r_2}=\frac{1}{2}$

Therefore, area of cross section

$\frac{A_1}{A_2}=\frac{r_1^2}{r_2^2}=\frac{1}{4}$

Thus,

$\frac{R_1}{R_2}=\frac{\rho_1}{\rho_2}\times\frac{l_1}{l_2}\times\frac{A_2}{A_1}$

$\frac{R_1}{R_2}=\frac{2}{3}\times \frac{3}{4}\times \frac{4}{1}$

$\implies \frac{R_1}{R_2}=\frac{2}{1}$

Thus the ratio of the resistances is 2:1

Hope this helps.