(d) total capacitance of two or more capacitors in parallel; C = C₁ + C₂ +…

The idea

When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitances: C = C₁ + C₂ + ... . This means the total capacitance is always greater than the largest individual capacitance. For example, two 10 μF capacitors in parallel give C = 10 + 10 = 20 μF. In a parallel arrangement, each capacitor has the same potential difference across it, and the total charge stored is the sum of the charges on the individual capacitors. The formula is used directly without taking reciprocals.

What earns the marks

• The formula for capacitors in parallel is C = C₁ + C₂ + ... .
• The total capacitance in parallel is greater than the largest individual capacitance.
• Each capacitor in parallel has the same potential difference across it.
• The total charge stored is the sum of the charges on the individual capacitors.
• The formula is applied by direct addition of the capacitance values.

Common mistakes and how to put them right

• Using reciprocals for parallel capacitors, as if they were in series.

  Put it right: Parallel uses direct addition.

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

  Put it right: In parallel it is always greater.

• Forgetting that the potential difference is the same across each parallel branch.

• Adding charges instead of capacitances when the question asks for total capacitance.

Exam tips

• Write down the formula C = C₁ + C₂ + ... before substituting values.
• Check that your answer is larger than the largest individual capacitance as a quick sanity check.
• Keep units consistent, for example all capacitances in μF or all in F.
• Remember that in parallel the potential difference across each capacitor is the same.