Resistance and resistivity

Resistance is a measure of how much a material opposes the flow of electric current. When a potential difference (voltage) is applied across a conductor, it causes a current to flow. The resistance determines how much current will flow for a given voltage.

Ohm’s Law

Ohm’s law states that, for a metallic conductor at constant temperature, the current through the conductor is directly proportional to the potential difference across it.

Where:

• $V$ = potential difference (volts, V)
• $I$ = current (amperes, A)
• $R$ = resistance (ohms, $\Omega$)

I–V Characteristics

The I–V characteristic of a component is a graph showing how current ($I$) varies with applied voltage ($V$).

• Metallic conductor at constant temperature: Straight line through the origin (obeys Ohm’s law).
• Filament lamp: Curve with decreasing gradient; as current increases, resistance increases due to heating.
• Semiconductor diode: Current flows only after a threshold voltage in one direction; almost zero current in reverse.

Resistance in Filament Lamps

As current increases in a filament lamp, the temperature of the filament rises. The increased temperature causes the resistance to increase, so the I–V graph curves and becomes less steep at higher currents.

Resistivity

Resistivity ($\rho$) is a property of a material that quantifies how strongly it resists current flow.

The resistance $R$ of a uniform wire depends on:

• Length ($L$): longer wires have more resistance
• Cross-sectional area ($A$): wider wires have less resistance
• Resistivity ($\rho$): a material constant

Where:

• $R$ = resistance ($\Omega$)
• $\rho$ = resistivity ($\Omega$ m)
• $L$ = length (m)
• $A$ = cross-sectional area ($m^2$)

Light-Dependent Resistor (LDR)

An LDR’s resistance decreases as the light intensity increases. More light releases more charge carriers, lowering resistance.

Thermistor

A thermistor is a resistor whose resistance decreases as temperature increases (negative temperature coefficient). Higher temperature gives more charge carriers, so resistance drops.

---

Summary Table: How resistance changes