A wire of resistance R and radius r is stretched till its radius became r/2. If new resistance of the stretched wire is x R. then value of x is

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Solution

Q.
A wire of resistance R and radius r is stretched till its radius became r/2. If new resistance of the stretched wire is x R. then value of x is _______ . [2024]

Ans.
(16) We know $R = \frac{ρ l}{A} \Rightarrow R \propto \frac{l}{r^{2}}$

  As we stretch the wire, its length will increase but its radius will decrease keeping the volume constant.

   $V_{i} = V_{f} \Rightarrow π r^{2} l = π \frac{r^{2}}{4} l_{f} \Rightarrow l_{f} = 4 l$

   $\frac{R_{n e w}}{R_{o l d}} = (\frac{4 l}{\frac{r^{2}}{4}}) \frac{r^{2}}{l} = 16$

$R_{n e w} = 16 R$

   $∴ x = 16$

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