A uniform wire of length l and radius r has a resistance of 100 Ω . It is recast into a wire of radius (r/2). The resistance of new wire will be :

Question

A uniform wire of length l and radius r has a resistance of 100 Ω . It is recast into a wire of radius (r/2). The resistance of new wire will be : (A) 1600 Ω (B) 400 Ω (C) 200 Ω (D) 100 Ω

Tardigrade Admin · Accepted Answer

R=(ρ l/A) A l=V R=(ρ v/A2) ρ arrow constant v arrow constant R propto (1/A2) propto (1/r2) R propto (1/r4) R2=16 R1=1600 Ω

Q. A uniform wire of length $l$ and radius $r$ has a resistance of $100 Ω$ . It is recast into a wire of radius $\frac{r}{2}$ . The resistance of new wire will be :

$1600 Ω$

$400 Ω$

$200 Ω$

$100 Ω$

$R = \frac{ρl}{A} A l = V$
$R = \frac{ρ v}{A ^{2}}$
$ρ \to$ constant
$v \to$ constant
$R \propto \frac{1}{A ^{2}} \propto \frac{1}{r ^{2}}$
$R \propto \frac{1}{r ^{4}}$
$R_{2} = 16 R_{1} = 1600 Ω$

Q. A uniform wire of length l and radius r has a resistance of 100Ω . It is recast into a wire of radius 2r​. The resistance of new wire will be :

1600Ω

400Ω

200Ω

100Ω