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

$(a)$ Three resistors $R_{1}, R_{2}$ and $R_{3}$ are connected in parallel and the combination is connected to a battery,ammeter,voltmeter,and key. Draw a suitable circuit diagram. Obtain an expression for the effective resistance of the combination of resistors in parallel.
$(b)$ Why are electric bulbs filled with chemically inactive nitrogen or argon?
$(c)$ What is meant by the statement that the rating of a fuse in a circuit is $5 \ A$?

Given below is a circuit showing current flowing in it. Identify each component $A, B, C, D$ of this circuit.

What is the $SI$ unit of electric charge?

Which effect of electric current is used in electroplating?

An electric geyser is connected to a $220 \; V$ line and consumes $4.4 \; kWh$ of electrical energy in $1 \; hour$. What is the resistance of the geyser?

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