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Q.
Two wires $A$ and $B$ of same material and same mass have radius $2 r$ and $r$. If resistance of wire $A$ is $34\, \Omega$, then resistance of $B$ will be
Current Electricity
Solution:
$R=\rho \frac{l}{A}$ and mass $m=$ volume $(V) \times$ density $(d)=$ $(A l) d$
Since wires have same material so $\rho$ and $d$ is same for both.
Also they have same mass $\Rightarrow A l=$ 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}{2 r}\right)^{4} $
$\Rightarrow R_{2}=544 \,\Omega$