(D) The slope of the $I-V$ curve is given by $\text{slope} = \frac{I}{V} = \frac{1}{R}$.Since resistance $R = \frac{\rho L}{A}$, we have $\text{slope}

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Less if the length of the wire is increased

(D) The slope of the $I-V$ curve is given by $\text{slope} = \frac{I}{V} = \frac{1}{R}$.Since resistance $R = \frac{\rho L}{A}$, we have $\text{slope} = \frac{1}{R} = \frac{A}{\rho L}$.From this expression, it is clear that the slope is inversely proportional to the length $L$ of the wire $(\text{slope} \propto \frac{1}{L})$.Therefore, if the length of the wire is increased, the slope of the curve will decrease.Thus, option $(d)$ is correct.

Class 12 Physics Current Electricity Resistance of wire, Resistivity and Conductivity

Easy

$I-V$ characteristic of a copper wire of length $L$ and area of cross-section $A$ is shown in the figure. The slope of the curve becomes

A
More if the experiment is performed at a higher temperature
B
More if a wire of steel of the same dimension is used
C
More if the length of the wire is increased
D
Less if the length of the wire is increased

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Current Electricity

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Resistance of wire, Resistivity and Conductivity

What is the resistance of a cubic block of length $50 \, cm$ having a resistivity of $50 \times 10^{-8} \, \Omega m$?

Easy

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Space between two concentric conducting spheres of radii $a$ and $b$ $(b > a)$ is filled with a medium of resistivity $\rho$. The resistance between the two spheres will be

DifficultJEE MAIN 2019

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Two different conductors have the same resistance at $0\,^{\circ}C$. The resistance of the first conductor at $t_1\,^{\circ}C$ is equal to the resistance of the second conductor at $t_2\,^{\circ}C$. What is the ratio of their temperature coefficients of resistance $\alpha_1 / \alpha_2$?

Medium

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Two conductors are made of the same material and have the same length. Conductor $A$ is a solid wire of diameter $1 \ mm$. Conductor $B$ is a hollow tube of outer diameter $2 \ mm$ and inner diameter $1 \ mm$. Find the ratio of resistance $R_A$ to $R_B$.

Medium

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$A$ $1\,m$ long wire is broken into two unequal parts $X$ and $Y$. The $X$ part of the wire is stretched into another wire $W$. The length of $W$ is twice the length of $X$ and the resistance of $W$ is twice that of $Y$. Find the ratio of the length of $X$ to the length of $Y$.

MediumJEE MAIN 2022

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$I-V$ characteristic of a copper wire of length $L$ and area of cross-section $A$ is shown in the figure. The slope of the curve becomes

Similar Questions

What is the resistance of a cubic block of length $50 \, cm$ having a resistivity of $50 \times 10^{-8} \, \Omega m$?

Space between two concentric conducting spheres of radii $a$ and $b$ $(b > a)$ is filled with a medium of resistivity $\rho$. The resistance between the two spheres will be

Two different conductors have the same resistance at $0\,^{\circ}C$. The resistance of the first conductor at $t_1\,^{\circ}C$ is equal to the resistance of the second conductor at $t_2\,^{\circ}C$. What is the ratio of their temperature coefficients of resistance $\alpha_1 / \alpha_2$?

Two conductors are made of the same material and have the same length. Conductor $A$ is a solid wire of diameter $1 \ mm$. Conductor $B$ is a hollow tube of outer diameter $2 \ mm$ and inner diameter $1 \ mm$. Find the ratio of resistance $R_A$ to $R_B$.

$A$ $1\,m$ long wire is broken into two unequal parts $X$ and $Y$. The $X$ part of the wire is stretched into another wire $W$. The length of $W$ is twice the length of $X$ and the resistance of $W$ is twice that of $Y$. Find the ratio of the length of $X$ to the length of $Y$.

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