Question

Two wires $A$ and $B$ of same material and same mass have radius $2r$ and $r$. If resistance of wire $A$ is $34\Omega$, then resistance of $B$ will be

• A. $544\Omega$
• B. $372\Omega$
• C. $68\Omega$
• D. $17\Omega$

Answer 1

Answer: (A)

$R=\rho \frac{l}{A}$ and mass $m=$ volume $(V)\times$ density $(d)=$ $(Al)d$
Since wires have same material so $\rho$ and $d$ is same for both.
Also they have same mass $\Rightarrow Al=$ constant
$\Rightarrow l\propto \frac{1}{A}$
$\Rightarrow \frac{R_1}{R_2}=\frac{l_1}{l_2}\times \frac{A_2}{A_1}={\left(\frac{A_2}{A_1}\right)}^2={\left(\frac{r_2}{r_1}\right)}^4$
$\Rightarrow \frac{34}{R_2}={\left(\frac{r}{2r}\right)}^4$
$\Rightarrow R_2=544\Omega$