Capacitors: (a) capacitance; C = Q/V; the unit farad

The idea

A capacitor stores charge on two conductors separated by an insulator. Its capacitance C is defined as the charge stored per unit potential difference: C = Q/V, where Q is the magnitude of charge on one plate and V is the potential difference across the capacitor. The unit of capacitance is the farad (F); one farad is one coulomb per volt, so 1 F = 1 C V⁻¹. Typical capacitors have values in microfarads (1 μF = 1 × 10⁻⁶ F), nanofarads (1 nF = 1 × 10⁻⁹ F) or picofarads (1 pF = 1 × 10⁻¹² F). Rearranged, Q = CV and V = Q/C.

What earns the marks

• Defines capacitance as charge stored per unit potential difference: C = Q/V.
• States that the unit of capacitance is the farad, where 1 F = 1 C V⁻¹.
• Uses the rearrangements Q = CV and V = Q/C correctly in calculations.
• Converts between farads and submultiples such as μF, nF and pF using powers of ten.

Common mistakes and how to put them right

• Using the total charge on both plates in C = Q/V.

  Put it right: Q is the magnitude of charge on one plate.

• Treating the farad as a base unit.

  Put it right: It is defined as one coulomb per volt.

• Mixing up microfarads and nanofarads, for example writing 1 μF = 1 × 10⁻⁹ F instead of 1 × 10⁻⁶ F.

• Substituting the potential difference across the whole circuit for the potential difference across the capacitor.

Exam tips

• Write the defining equation C = Q/V before substituting values so the quantities are clear.
• Convert all capacitance values to farads before calculating, then convert the answer back if needed.
• Check units: charge in coulombs, potential difference in volts and capacitance in farads.