(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

By increasing the temperature,the specific resistance (resistivity) of a conductor and a semiconductor,respectively,is:

EasyAIEEE 2002

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The resistivity of a material is found to be $10^8 \Omega \cdot m$. Then the material would be

EasyTS EAMCET 2022

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Which of the following resistivity ( $\rho$ ) $v/s$ temperature $( T )$ curves is most suitable to be used in wire-bound standard resistors?

MediumJEE MAIN 2025

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The coefficient of linear expansion of the material of a resistor is $\alpha$. Its temperature coefficient of resistivity and resistance are $\alpha_\rho$ and $\alpha_R$ respectively. Then the correct relation is:

Difficult

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$A$ wire $50\, cm$ long and $1\, mm^2$ in cross-section carries a current of $4\, A$ when connected to a $2\, V$ battery. The resistivity of the wire is:

MediumAIPMT 1994

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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

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By increasing the temperature,the specific resistance (resistivity) of a conductor and a semiconductor,respectively,is:

The resistivity of a material is found to be $10^8 \Omega \cdot m$. Then the material would be

Which of the following resistivity ( $\rho$ ) $v/s$ temperature $( T )$ curves is most suitable to be used in wire-bound standard resistors?

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