9.3 Resistance and Resistivity

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Define resistance
  2. Recall and use V = IR
  3. Sketch the I–V characteristics of a metallic conductor at constant temperature, a semiconductor diode, and a filament lamp
  4. Explain that the resistance of a filament lamp increases as current increases because its temperature increases
  5. State Ohm's law
  6. Recall and use R = ρL/A
  7. Understand that the resistance of an LDR decreases as light intensity increases
  8. Understand that the resistance of a thermistor decreases as temperature increases (negative temperature coefficient)

1. Defining Resistance

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Resistance is the opposition to the flow of electric current. Think of it like friction — the higher the resistance in a component, the harder it is for current to flow through it.

  • A high resistance means a small current flows for a given voltage.
  • A low resistance means a large current flows for the same voltage.
  • Every component in a circuit — including wires — has some resistance.
  • Copper wire is commonly used in electrical cables because copper has a very low resistance, meaning current flows through it easily.

The Resistance Equation

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

SymbolQuantityUnit
RResistanceOhm (Ω)
VPotential difference (voltage)Volt (V)
ICurrentAmpere (A)

Key fact: 1 Ω = 1 V A⁻¹ (one ohm equals one volt per ampere)

This can be rearranged to:

V=IRorI=VRV = IR \quad \text{or} \quad I = \frac{V}{R}

Worked Example

A charge of 5.0 C passes through a resistor at a constant rate in 30 s. The potential difference across the resistor is 2.0 V. Calculate the resistance.

Step 1: Find the current. We know that charge Q = I × t, so:

I=Qt=5.030=0.17 AI = \frac{Q}{t} = \frac{5.0}{30} = 0.17 \text{ A}

Step 2: Use the resistance equation:

R=VI=2.00.17=12 ΩR = \frac{V}{I} = \frac{2.0}{0.17} = 12 \text{ Ω}

2. Ohm's Law

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Ohm's law states:

For a conductor at constant temperature, the current through it is directly proportional to the potential difference across it.

In plain English: if you double the voltage across a resistor (while keeping its temperature the same), the current through it also doubles. The resistance stays constant.

This means V ∝ I, or equivalently: V = IR (where R is a fixed constant).

  • A component obeys Ohm's law if its I–V graph is a straight line through the origin.
  • A component that obeys Ohm's law is called an ohmic conductor.
  • Components that do not produce a straight-line I–V graph are called non-ohmic conductors.

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