The $V-I$ graphs for two resistors of the same material and the same radii with lengths $L_{1}$ and $L_{2}$ are shown below. If $L_{1} > L_{2}$, state with reason, which of these graphs represents voltage-current change for $L_{1}$?

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(B) The resistance $R$ of a conductor is given by $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity, $L$ is the length, and $A$ is the cross-sectional area.
Since both resistors are made of the same material ($\rho$ is constant) and have the same radii ($A$ is constant), the resistance $R$ is directly proportional to the length $L$ $(R \propto L)$.
Given $L_{1} > L_{2}$, it follows that $R_{1} > R_{2}$.
In a $V-I$ graph, the slope represents the resistance $(R = \frac{V}{I} = \text{slope})$. A steeper slope indicates a higher resistance.
Comparing the two graphs, graph $B$ has a greater slope than graph $A$, meaning the resistance of graph $B$ is greater than that of graph $A$.
Since $R_{1} > R_{2}$, graph $B$ corresponds to the longer length $L_{1}$.

Explore More

Similar Questions

$A$ series circuit has only one conducting path for the electrons that move through it; a parallel circuit has multiple conducting paths.

What will be the equivalent resistance between points $A$ and $B$ of the following electric circuit?

Which physical quantity has a unit of $kWh$?

Three incandescent bulbs of $100\, W$ each are connected in series in an electric circuit. In another circuit,another set of three bulbs of the same wattage are connected in parallel to the same source. Now,if one bulb in both the circuits gets fused,will the rest of the bulbs continue to glow in each circuit? Give reasons.

Electric power of a circuit is the rate at which work is done in maintaining the electric current in the circuit.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo