Overview
This lecture explains the concepts of capacitors in series, parallel, and mixed (series-parallel) circuits, including formulas for calculating equivalent capacitance, charge, voltage, and stored energy.
Series Capacitor Circuits
- In a series circuit, capacitors are connected end to end (C1, C2, C3, etc.).
- The reciprocal of the equivalent capacitance: 1/C_eq = 1/C1 + 1/C2 + 1/C3 + ...
- Charge (Q) on all capacitors is the same in series.
- The total voltage is the sum: V_total = V1 + V2 + V3.
- Voltage across each capacitor: V = Q/C.
- Stored energy: W = ½ CV² or ½ QV.
Parallel Capacitor Circuits
- In parallel, capacitors are connected across the same two points.
- Equivalent capacitance: C_eq = C1 + C2 + C3 + ...
- Voltage across each capacitor is the same (V_total).
- Total charge: Q_total = Q1 + Q2 + Q3.
- Charge for each: Q = C × V.
- Stored energy formula is the same: W = ½ CV² or ½ QV.
Mixed Series-Parallel Circuits
- Combine series and parallel rules to simplify complex circuits step by step.
- Reduce series and parallel parts separately to calculate overall C_eq.
- Calculate total and individual capacitor charge and voltage using equivalent values.
- Stored energy can be found using the formulas above for the relevant part of the circuit.
Worked Examples Summary
- Series: For three capacitors (2μF, 3μF, 6μF) in series with 18V, C_eq = 1μF, Q = 18μC, voltage division calculated for each.
- Parallel: For three capacitors (3μF, 5μF, 2μF) in parallel with 20V, C_eq = 10μF, Q_total = 200μC, each capacitor gets 20V, charge calculated individually.
- Mixed: Reducing series and parallel combinations to find C_eq, Q, V, and W for each capacitor using the steps above.
Key Terms & Definitions
- Capacitor — An electronic component that stores electrical energy.
- Capacitance (C) — The ability of a capacitor to store charge, measured in farads (F).
- Equivalent Capacitance (C_eq) — The capacitance of a single capacitor that could replace a combination.
- Charge (Q) — The amount of electricity stored, measured in coulombs (C).
- Voltage (V) — The electric potential difference across a capacitor.
- Energy Stored (W) — The electrical energy stored in a capacitor, measured in joules (J).
Action Items / Next Steps
- Practice simplifying series, parallel, and mixed capacitor circuits.
- Solve problems to calculate C_eq, Q, V, and W for various circuit configurations.