Capacitors store electric charge and energy in electric fields, so they appear in timing circuits, filters, camera flashes, power supplies, and touch screens. When more than one capacitor is connected in a circuit, the combination can behave like one equivalent capacitor. Series and parallel connections follow different rules because charge and voltage distribute differently.
Understanding these rules helps you simplify circuits and predict how much energy they can store.
In a series connection, capacitors are linked end to end, so the same charge appears on each capacitor and the battery voltage is shared among them. In a parallel connection, each capacitor is connected across the same two nodes, so each has the same voltage and the charges add. The equivalent capacitance in parallel is larger than any single capacitor, while the equivalent capacitance in series is smaller than the smallest capacitor.
Energy stored can be found from E = 1/2 CV^2 once the voltage across a capacitor or equivalent capacitor is known.
Key Facts
- Capacitance is defined by C = Q/V, where Q is charge and V is voltage.
- For capacitors in parallel: C_eq = C1 + C2 + C3 + ...
- For capacitors in series: 1/C_eq = 1/C1 + 1/C2 + 1/C3 + ...
- In series, each capacitor has the same charge: Q1 = Q2 = Q3 = Q_eq.
- In parallel, each capacitor has the same voltage: V1 = V2 = V3 = V_battery.
- Energy stored in a capacitor is E = 1/2 CV^2 = Q^2/(2C) = 1/2 QV.
Vocabulary
- Capacitor
- A capacitor is a circuit component that stores electric charge and energy in an electric field between two conducting plates.
- Capacitance
- Capacitance is the ability of a capacitor to store charge per volt, measured in farads.
- Equivalent capacitance
- Equivalent capacitance is the single capacitance value that would have the same overall effect as a group of connected capacitors.
- Series connection
- A series connection places components along one path so the same charge must pass through each capacitor plate pair.
- Parallel connection
- A parallel connection places components across the same two nodes so each capacitor has the same voltage across it.
Common Mistakes to Avoid
- Adding series capacitors like resistors is wrong because capacitors in series combine by reciprocal sum, so the equivalent capacitance gets smaller.
- Assuming voltage is the same across series capacitors is wrong because series capacitors share charge equally, while their voltages depend on their capacitances.
- Assuming charge is the same on parallel capacitors is wrong because parallel capacitors share voltage equally, and larger capacitance stores more charge at that voltage.
- Forgetting units such as microfarads is wrong because 1 microfarad equals 1 x 10^-6 farad, and missing this conversion can change answers by a factor of one million.
Practice Questions
- 1 Two capacitors, 6.0 microfarads and 3.0 microfarads, are connected in series to a 12 V battery. Find the equivalent capacitance, the charge on each capacitor, and the voltage across each capacitor.
- 2 Three capacitors, 2.0 microfarads, 4.0 microfarads, and 6.0 microfarads, are connected in parallel to a 9.0 V battery. Find the equivalent capacitance, the charge on each capacitor, and the total energy stored.
- 3 A 2.0 microfarad capacitor and an 8.0 microfarad capacitor are connected first in series and then in parallel to the same battery. Explain which arrangement stores more total energy and why.