(a) State Ohm's Law. Represent it mathematically.

(b) Define 1 ohm.

(c) What is the resistance of a conductor through which a current of $0.5\text{ A}$ flows when a potential difference of $2\text{ V}$ is applied across its ends ?

(a) Ohm's Law: The potential difference, $V$, across the ends of a given metallic wire in an electric circuit is directly proportional to the current, $I$, flowing through it, provided its temperature remains the same.

Mathematical Representation:

$$V \propto I$$

$$V = IR$$

where $R$ is a constant for the given metallic wire at a given temperature and is called its resistance.

(b) Definition of $1\ \Omega$: One ohm ($1\ \Omega$) is the resistance of a conductor such that when a potential difference of $1\text{ V}$ is applied across its ends, a current of $1\text{ A}$ flows through it.

$$1\ \Omega = \frac{1\text{ volt}}{1\text{ ampere}} = 1\text{ V A}^{-1}$$

(c) Calculation of Resistance:

Given:

• Current, $I = 0.5\text{ A}$
• Potential difference, $V = 2\text{ V}$

Using Ohm's Law:

$$R = \frac{V}{I} = \frac{2\text{ V}}{0.5\text{ A}} = 4\ \Omega$$

Therefore, the resistance of the conductor is $4\ \Omega$.