Current, resistance and potential difference: potential difference = current × resistance

The idea

This relationship links the potential difference across a component, the current through it and its resistance. Potential difference (V) is the energy transferred per unit charge, measured in volts (V). Current (I) is the rate of flow of charge, measured in amperes (A). Resistance (R) is the opposition to current, measured in ohms (Ω). For a fixed resistance, increasing the potential difference increases the current in direct proportion.

For example: A resistor of 20 Ω with a current of 0.30 A has V = 0.30 × 20 = 6.0 V. Rearranged, I = V ÷ R and R = V ÷ I. This applies to ohmic conductors at constant temperature; filament lamps and diodes behave non-linearly, so the equation describes the value at a particular point rather than a constant ratio.

What earns the marks

• State the equation as potential difference = current × resistance and identify the correct SI units: volts (V), amperes (A) and ohms (Ω).
• Substitute numerical values correctly into V = I R, including values given in mA or kΩ after converting to A and Ω.
• Rearrange the equation to find current (I = V ÷ R) or resistance (R = V ÷ I) without arithmetic errors.
• Interpret the result in context, for example stating that a larger resistance at the same potential difference gives a smaller current.
• Recognise that the equation applies to ohmic conductors at constant temperature and that non-ohmic components may not obey a constant resistance.

Common mistakes and how to put them right

• Mixing up the subject of the formula, for example calculating I × R when asked for current.

  Put it right by rearranging to I = V ÷ R before substituting.

• Forgetting to convert milliamperes to amperes or kilohms to ohms.

  Put it right by multiplying mA by 10⁻³ and kΩ by 10³ before calculating.

• Assuming resistance is always constant for every component.

  Put it right by noting that filament lamps and diodes are non-ohmic and their resistance changes with current or temperature.

Exam tips

• Write the equation, then substitute values with units before doing the arithmetic so the examiner can follow your method.
• Check the unit of every quantity and convert to A and Ω before calculating; give the final answer with the correct unit.
• For a 'show that' or explain question, quote the rearranged equation and comment on the effect of changing one variable while another is fixed.