Capacitors in parallel
In parallel the capacitances add: C = C₁ + C₂ + C₃. For 2, 3 and 6 μF, C = 11 μF; on 12 V they hold 24, 36, 72 μC, 132 μC in all.
Capacitors
In series the charge is the same on each and 1/C = 1/C₁ + 1/C₂ + 1/C₃. In parallel the voltage is the same and C = C₁ + C₂ + C₃. Energy U = ½CV². Leave a box empty to use fewer capacitors.
In parallel11 μF
Charge132 μC
Energy792 μJ
- C₁, C₂, C₃ in parallel: C = 2 + 3 + 6 = 11 μF
- Charge from the cell: Q = CV = 11 × 12 = 132 μC
- In parallel every capacitor has the same 12 V, so Q = CV splits the charge: C₁: 24 μC, C₂: 36 μC, C₃: 72 μC.
- Energy stored: U = ½CV² = ½ × 11 × 12² = 792 μJ
Why it works
- In parallel every capacitor is across the same two points, so each has the same voltage V.
- The charges are Q₁ = C₁V, Q₂ = C₂V and Q₃ = C₃V.
- The total charge drawn from the cell is Q = Q₁ + Q₂ + Q₃ = (C₁ + C₂ + C₃)V.
- For the single equivalent capacitor Q = CV, so C = C₁ + C₂ + C₃.
- C in parallel is larger than the largest capacitor, the same rule as resistors in series.
Capacitors in parallel: quick answers
What is the equivalent of 2, 3 and 6 μF in parallel?
C = 2 + 3 + 6 = 11 μF.
Which capacitor in parallel holds the most charge?
The largest one, since Q = CV with the same V on each. Here 6 μF holds 72 μC.
How does a parallel combination compare with a series one?
Parallel adds the capacitances and gives the largest total. Series adds the reciprocals and gives a total smaller than any one. For 2, 3 and 6 μF that is 11 μF against 1 μF.