Question

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

• A. $1600 \, \Omega$
• B. $400 \, \Omega$
• C. $200 \, \Omega$
• D. $100 \, \Omega$

Answer 1

Answer: (A)

$1600 \, \Omega$

Answer 2

$R=\frac{\rho l}{A} \,\,\,\,\,A l=V$
$R=\frac{\rho v}{A^{2}}$
$\rho \rightarrow$ constant
$v \rightarrow$ constant
$R \propto \frac{1}{A^{2}} \propto \frac{1}{r^{2}}$
$R \propto \frac{1}{r^{4}}$
$R_{2}=16 \,R_{1}=1600 \,\Omega$