Electric Resistance

When current flows through a conductor, the material offers some opposition to the flow of electrons — much like friction opposes motion. This opposition is called electric resistance.

Understanding resistance is fundamental to analysing circuits, designing electrical appliances, and solving nearly every numerical problem in the Current Electricity unit.

Think of a wire as a water pipe. Current is like water flow, voltage is like water pressure, and resistance is like the pipe's narrowness — a narrower pipe (higher resistance) allows less water (current) to flow for the same pressure (voltage).

Electric resistance is the property of a conductor by virtue of which it opposes the flow of electric current through it.

R = \[\frac {V}{I}\]

Resistivity is a material-dependent property that measures how strongly a material opposes current flow, independent of its shape or size.

ρ = \[\frac {RA}{l}\]

Conductance is the reciprocal of resistance — a measure of how easily current flows through a conductor.

G = \[\frac {1}{R}\]

Resistance of a conductor depends on:

• Length (l): Directly proportional — longer wire, more resistance.
• Area of cross-section (A): Inversely proportional — thicker wire, less resistance.
• Material (ρ): Different materials have different resistivities.
• Temperature: Resistance of metals increases with temperature; resistance of semiconductors decreases.
  R = ρ\[\frac {l}{A}\]
• Resistance does not depend on the values of V or I applied, only on material, dimensions, and temperature — under fixed physical conditions.

Example 1: A conductor has a potential difference of 30 V across it and carries a current of 2 A. Find its resistance.

R = \[\frac {V}{I}\] = \[\frac {30}{2}\] = 15 Ω