Recall and use the equation for resistance R = V / I

4.2.4 Resistance

Learning Objective (Core)

Recall and use the equation for resistance:

R = V ⁄ I

Definition (Cambridge IGCSE 0625)

Resistance (R) is the opposition to the flow of electric current. It is a property of a material and is measured in ohms (Ω).

Core Relationships

• Ohm’s law: \(V = I R\)
• Re‑arranged for resistance: \(R = \dfrac{V}{I}\)

Supplementary – Resistivity Formula (not required for the core syllabus)

For deeper study you may use the resistivity relationship:

\[ R = \rho \frac{L}{A} \]

• \(\rho\) – resistivity of the material (Ω·m)
• L – length of the conductor (m)
• A – cross‑sectional area (m²)

Factors that Influence the Resistance of a Metallic Wire (qualitative relationships)

1. Length (L) – resistance is directly proportional to length.
   R ∝ L
2. Cross‑sectional area (A) – resistance is inversely proportional to area.
   R ∝ 1/A
3. Material – different materials have characteristic resistivities (ρ). A material with a lower ρ (e.g. copper) gives a lower resistance than one with a higher ρ (e.g. nichrome) for the same L and A.
4. Temperature (T) – for most metals, resistance increases approximately linearly with temperature:
   \[ R \approx R_{0}\,[1+\alpha\,(T-T_{0})] \] where \(\alpha\) is the temperature coefficient of resistance (°C⁻¹).
   Example: for copper \(\alpha \approx 0.004\ \text{°C}^{-1}\). If a copper wire has \(R_{0}=2.0\ \Omega\) at \(20^{\circ}\text{C}\), its resistance at \(70^{\circ}\text{C}\) is \(R = 2.0[1+0.004(70-20)] = 2.0[1+0.20] = 2.4\ \Omega\).

Using the Equation \(R = \dfrac{V}{I}\) (Core)

To find any one of the three quantities (voltage, current, resistance) you need the other two.

Standard Experiment to Determine Resistance (AO2/AO3)

1. Connect the ammeter in series with the unknown resistor and the battery. (AO3 – planning and setting up the circuit)
2. Connect the voltmeter across (parallel to) the resistor. (AO3 – correct use of measuring instruments)
3. Switch on the circuit and record the voltage reading (V) and the current reading (I). (AO2 – recording data)
4. Calculate the resistance with \(R = V/I\). (AO2 – data analysis)
5. Repeat with at least two different battery voltages. Check that V and I are proportional; a straight‑line V‑I plot confirms ohmic behaviour. (AO3 – evaluating the investigation)

Current‑Voltage Graphs (Supplementary)

Understanding V‑I graphs helps to see when the simple relation \(R = V/I\) is valid.

• Ohmic resistor – straight line through the origin. Gradient = R (Ω).
  
• Filament lamp (non‑ohmic) – curve that becomes steeper as V increases because the filament heats up and its resistance rises.
  
• Diode (non‑ohmic) – almost no current until a “forward voltage” is reached, then current rises sharply.
  

Why \(R = V/I\) is not always constant

For an ohmic resistor the gradient of the straight‑line V‑I graph is constant, so \(R\) is the same at all points. For a filament lamp or a diode the graph is curved; the “resistance” calculated at one point ( \(R = V/I\) ) differs from that calculated at another point because the material’s resistance changes with temperature or with the applied voltage.

Link to Power (Core)

Because resistance determines how much electrical energy is converted to heat, the power dissipated in a resistor is:

\[ P = I^{2}R = \frac{V^{2}}{R} = VI \]

This relationship is examined later in the IGCSE topic “Electrical Power”.

Safety Reminder (AO3)

• Never connect a voltmeter directly across a live source without a series resistor – this can cause a short circuit.
• Always switch off the circuit before changing connections.
• Handle hot wires with insulated pliers and keep the work area dry.
• Use the correct rating for ammeters and voltmeters; exceeding their limits can damage the instrument and create a hazard.

Quick Revision Table (Core)