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 $\qquad$
JEE MAIN 2024, Diffcult
Download our app for free and get started
We know $\mathrm{R}=\frac{\rho l}{\mathrm{~A}}, \mathrm{R} \propto \frac{l}{\mathrm{r}^2}$
As we starch the wire, its length will increase but its radius will decrease keeping the volume constant
$\mathrm{V}_{\mathrm{i}}=\mathrm{V}_{\mathrm{f}}$
$\pi^2 l=\pi \frac{\mathrm{r}^2}{4} l_{\mathrm{f}}$
$l_{\mathrm{f}}=4 l$
$\frac{\mathrm{R}_{\text {nelv }}}{\mathrm{R}_{\text {old }}}=\left(\frac{4 l}{\frac{\mathrm{r}^2}{4}}\right) \frac{\mathrm{r}^2}{l}=16$
$\mathrm{R}_{\text {neer }}=16 \mathrm{R}$
$\therefore \mathrm{x}=16$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Two ideal batteries of emf $V _1$ and $V _2$ and three resistances $R _1, R _2$ and $R _3$ are connected as shown in the figure.View Solution
The current in resistance $R _2$ would be zero if
$(A)$ $V_1=V_2$ and $R_1=R_2=R_3$
$(B)$ $V_1=V_2$ and $R_1=2 R_2=R_3$
$(C)$ $V_1=2 V_2$ and $2 R_1=2 R_2=R_3$
$(D)$ $2 V _1= V _2$ and $2 R _1= R _2= R _3$
- 2A wire of length ' $r$ ' and resistance $100 \Omega$ is divided into $10$ equal parts. The first $5$ parts are connected in series while the next $5$ parts are connected in parallel. The two combinations are again connected in series. The resistance of this final combination is:View Solution
- 3Two electric bulbs whose resistances are in the ratio of $1 : 2$ are connected in series. The powers dissipated in them have the ratioView Solution
- 4Figure shows a thick shell made of electrical conductivity $\sigma$ and has inner & outer radii of $10\ cm$ & $20\ cm$ respectively and is filled with ice inside it. Its inside and outside surface are kept at different potentials by a battery of internal resistance $\frac{2}{\pi} \Omega \ \&\ \in = 5V$. Find value of $\sigma$ for which ice melts at maximum possible rate if $25\%$ of heat generated by shell due to joule heating is used to melt ice.View Solution
- 5The current $i_1$ and $i_2$ through the resistors $R_1(=10\,\Omega )$ and ${R_2}\left( { = 30\,\Omega } \right)$ in the circuit diagram with $E_1 = 3\,V$, $E_2 = 3\,V$ and $E_3 = 2\,V$ are respectivelyView Solution
- 6As shown in the schematic below, a rod of uniform cross-sectional area $A$ and length $l$ is carrying a constant current $i$ through it and voltage across the rod is measured using an ideal voltmeter. The rod is stretched by the application of a force $F$. Which of the following graphs would show the variation in the voltage across the rod as function of the strain $\varepsilon$ when the strain is small. Neglect Joule heating.View Solution
- 7In the Wheatstone's bridge (shown in figure) $X = Y$ and $A > B$. The direction of the current between ab will beView Solution
- 8In the given figure, there is a circuit of potentiometer of length $A B=10 \,{m}$. The resistance per unit length is $0.1 \,\Omega$ per ${cm}$. Across ${AB}$, a battery of emf ${E}$ and internal resistance ' ${r}^{\prime}$ is connected. The maximum value of emf measured by this potentiometer is : (In $V$)View Solution
- 9View SolutionThe internal resistance of a cell depends on
- 10The equivalent resistance between points $A$ and $B$ in the given network is ............ $\Omega$View Solution
