(c) total capacitance of two or more capacitors in series; 1/C = 1/C₁ +…

The idea

When capacitors are connected in series, the reciprocal of the total capacitance equals the sum of the reciprocals of the individual capacitances: 1/C = 1/C₁ + 1/C₂ + ... . This means the total capacitance is always less than the smallest individual capacitance. For example, two 10 μF capacitors in series give 1/C = 1/10 + 1/10 = 2/10, so C = 5 μF. The same charge Q is stored on each capacitor in series, and the potential differences add to the supply p.d. The formula must be rearranged to find C after summing the reciprocals.

What earns the marks

• The formula for capacitors in series is 1/C = 1/C₁ + 1/C₂ + ... .
• The total capacitance in series is less than the smallest individual capacitance.
• Each capacitor in series stores the same magnitude of charge.
• The potential differences across capacitors in series add to give the total potential difference.
• To find C, calculate the sum of reciprocals and then take the reciprocal of that sum.

Common mistakes and how to put them right

• Adding capacitances directly for series, as if they were resistors in parallel.

  Put it right: The correct relationship uses reciprocals.

• Forgetting to take the reciprocal of the sum to obtain C.

  Put it right: The formula gives 1/C, not C.

• Assuming the total capacitance is greater than the largest individual capacitance.

  Put it right: In series it is always less than the smallest.

• Mixing up the series and parallel formulas.

  Put it right: Series uses reciprocals, parallel uses direct addition.

Exam tips

• Write down the formula 1/C = 1/C₁ + 1/C₂ + ... before substituting values.
• After summing reciprocals, remember to invert the result to find C.
• Check that your answer is smaller than the smallest individual capacitance as a quick sanity check.
• Keep units consistent, for example all capacitances in μF or all in F.