Class 11> Unit # 10: DC Circuits > Ohm's Law

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Ohm's Law and Resistance

Ohm's Law

Statement

"The current through a conductor is directly proportional to the potential difference between the ends of the conductor provided the physical conditions of the conductor remain the same."

If $I$ is the current passing through a conductor and $V$ is the potential difference between its ends, then according to Ohm's law:

$$I \propto V$$

$$I = K V \quad \text{--- (i)}$$

Where $K$ is a constant known as the conductance of the material of the conductor. Its value is different for different materials. The reciprocal of conductance is called electric resistance ($R$), i.e.:

$$R = \frac{1}{K} \quad \text{or} \quad K = \frac{1}{R}$$

Substituting $K = \frac{1}{R}$ into equation (i):

$$I = \frac{1}{R} V$$

$$V = I R$$

This equation is known as Ohm's Law.

Electric Resistance

Resistance is defined as the ratio of the potential difference applied across a conductor to the current passing through it. Mathematically:

$$R = \frac{V}{I}$$

Its SI unit is the Ohm ($\Omega$).

Definition of One Ohm

One ohm is the resistance of a conductor through which a current of $1\text{ A}$ passes when a potential difference of $1\text{ V}$ is maintained across the ends of the conductor.

Multiples and Sub-multiples of Ohm

• Kilohm ($\text{k}\Omega$): $1\text{ k}\Omega = 10^3\,\Omega$
• Megohm ($\text{M}\Omega$): $1\text{ M}\Omega = 10^6\,\Omega$
• Milliohm ($\text{m}\Omega$): $1\text{ m}\Omega = 10^{-3}\,\Omega$
• Microhm ($\mu\Omega$): $1\text{ }\mu\Omega = 10^{-6}\,\Omega$

Fig: Linear V-I characteristic curve verifying Ohm's Law for a metallic conductor.

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