Question

$I-V$ 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 a wire of steel of the same dimension is used
• B. more if the length of the wire is increased
• C. less if the length of the wire is increased
• D. more if the experiment is performed at higher temperature

Answer 1

The correct option is C less if the length of the wire is increased

Step 1: Find dependence of slope

For $I-V$ characteristic

Slope $=\frac{I}{V}=\frac{1}{R}=\frac{A}{\rho l}\dots \left(i\right)$



Step 2: choose correct option

From equation (i)

At higher temperature,

R will increase $\Rightarrow$ Slope will decrease

Option (a) is incorrect.

For the same dimension, Slope will remain the same

$\Rightarrow$ Option (b) is incorrect.

For increase in length of the wire,

Slope is inversely proportional to length
So, with increase in length, slope will decrease.

$\Rightarrow$ Option (c) is incorrect.

Hence, Option (d) is correct.