Chapter 11 · Question 3

State Ohm's law. What does a V-I graph for a metallic conductor look like, and what does it indicate?

Answer Revealed

Direct Answer:

Ohm's law states that the potential difference

V

across the ends of a given metallic conductor in an electric circuit is directly proportional to the current

I

flowing through it, provided its temperature remains constant (

V \propto I

, or

V = IR

). The V-I graph is a straight line passing through the origin, indicating that

V/I

(or

R

) is constant.

Simple Explanation

Ohm's law says voltage and current are proportional — double the voltage and the current doubles too, as long as the temperature stays the same. When you plot V against I for a wire, you get a straight line through the origin. The slope of that line is the resistance — a steeper line means more resistance.

Exam-Ready Structure

Ohm's law is a fundamental relationship in electric circuits: 1. Statement: At constant temperature, the potential difference (

V

) across the ends of a given conductor is directly proportional to the electric current (

I

) flowing through it. Mathematically,

V \propto I

, or

V / I = \text{constant}

, or

V = IR

, where

R

is a constant called resistance. 2. The SI unit of resistance is the ohm (represented by the Greek letter

\Omega

). One ohm is the resistance of a conductor such that a current of 1 A flows through it when a potential difference of 1 V is applied across its ends (

1\ \Omega = 1\ \text{V} / 1\ \text{A}

). 3. V-I graph: When potential difference (

V

) is plotted on the y-axis against current (

I

) on the x-axis for a metallic conductor obeying Ohm's law, the graph is a straight line passing through the origin. 4. Interpretation: The straight-line nature indicates that the ratio

V/I

is constant (the resistance

R

is constant) for different values of current. The slope of the V-I graph gives the resistance of the conductor. A steeper slope indicates higher resistance. 5. It is important to note that Ohm's law holds only when the temperature and other physical conditions of the conductor remain constant.

Key Points

Ohm's law: $V \propto I$ at constant temperature ( $V = IR$ )
Resistance $R = V / I$ ; SI unit is ohm ( $\Omega$ )
A V-I graph for an ohmic conductor is a straight line through the origin
The slope of the V-I graph gives the resistance of the conductor
Ohm's law is valid only at constant temperature

State Ohm's law. What does a V-I graph for a metallic conductor look like, and what does it indicate?