The masses of three wires of copper are in the ratio of 1:3:5 and their lengths are in the ratio 5:3:1 . The ratio of their electrical resistances is :-

Question

The masses of three wires of copper are in the ratio of 1:3:5 and their lengths are in the ratio 5:3:1 . The ratio of their electrical resistances is :- (A) 1:3:5 (B) 5:3:1 (C) 1:15:125 (D) 125:15:1

Tardigrade Admin · Accepted Answer

R=ρ (l/π r2) and m=π r2ld ∴ R propto (ℓ 2/ m) ∴ R1:R2:R3=(25/1):(9/3):(1/5)=125:15:1

Q. The masses of three wires of copper are in the ratio of $1 : 3 : 5$ and their lengths are in the ratio $5 : 3 : 1$ . The ratio of their electrical resistances is :-

$1 : 3 : 5$

$5 : 3 : 1$

$1 : 15 : 125$

$125 : 15 : 1$

$R = ρ \frac{l}{π r ^{2}}$ and $m = π r^{2} l d$
$∴ R \propto \frac{ℓ ^{2}}{m}$
$∴ R_{1} : R_{2} : R_{3} = \frac{25}{1} : \frac{9}{3} : \frac{1}{5} = 125 : 15 : 1$

Q. The masses of three wires of copper are in the ratio of 1:3:5 and their lengths are in the ratio 5:3:1 . The ratio of their electrical resistances is :-

1:3:5

5:3:1

1:15:125

125:15:1