Resistance: (a) resistance; R = V/I; the unit ohm

The idea

Resistance measures how difficult it is for current to flow through a component. It is defined by R = V/I, where V is the potential difference across the component and I is the current through it. The unit of resistance is the ohm, symbol Ω; one ohm is one volt per ampere. For example, if a potential difference of 6.0 V drives a current of 2.0 A through a resistor, its resistance is R = 6.0 V ÷ 2.0 A = 3.0 Ω. Resistance is not a fixed property of every component: for a filament lamp it changes as the current changes, so R = V/I gives the resistance at that particular operating point. In calculations, rearrange R = V/I to V = IR or I = V/R as needed, and always use the potential difference across the component, not the e.m.f. of the whole circuit.

What earns the marks

• Resistance is defined as R = V/I, where V is the potential difference across the component and I is the current through it.
• The unit of resistance is the ohm (Ω), equivalent to one volt per ampere (V A⁻¹).
• Rearranging R = V/I gives V = IR and I = V/R.
• Resistance may vary with operating conditions for non-ohmic components, so R = V/I gives the resistance at a particular point.
• In circuit calculations, use the potential difference across the component, not the supply e.m.f., unless they are the same.

Common mistakes and how to put them right

• Using the e.m.f. of the supply instead of the potential difference across the component.

  Put it right: Identify the voltage across the component itself.

• Writing the unit as V A instead of V A⁻¹.

  Put it right: The ohm is volts per ampere, so the unit is V A⁻¹.

• Assuming resistance is always constant for every component.

  Put it right: For a filament lamp or diode, resistance changes with current or voltage.

• Confusing resistance with resistivity.

  Put it right: Resistance depends on the component and its dimensions, while resistivity is a property of the material.

Exam tips

• Write down R = V/I before substituting values so the rearrangement is clear.
• Check that the current is in amperes and the potential difference in volts before dividing.
• If a graph of V against I is given, the resistance at a point is V/I, not the gradient unless the graph is linear through the origin.
• Give the unit with the numerical answer, for example 3.0 Ω.