Overview
This lecture covers the fundamentals of capacitors, including their structure, function, calculations related to charge and energy, combinations in circuits, charge redistribution, and discharge behavior.
Introduction to Capacitors
- A capacitor stores electrical charge and energy in a circuit using two conductive plates separated by an insulator (dielectric).
- Capacitors provide quick energy bursts, stabilize voltage, and are used in devices like camera flashes.
Structure and Charging Process
- Capacitors have two metal plates, circuit leads, and a dielectric material that allows an electric field but not charge flow.
- Before connection, plates are neutral; connecting to a battery moves electrons, creating equal and opposite charges on each plate.
- Charging continues until the capacitor voltage equals the battery voltage, forming an electric field that stores energy.
Capacitance and Stored Charge
- Capacitance (C) is the charge stored per unit voltage, measured in farads (F), often microfarads (μF) or nanofarads (nF).
- Charge stored (Q) is calculated by Q = C × V.
- Each capacitor has a maximum voltage rating to prevent breakdown.
Energy Storage in Capacitors
- Work is required to move charge onto the plates; as charge increases, it becomes harder to add more.
- Energy stored (W) can be calculated by:
- W = ½ C V²
- W = ½ Q V
- W = ½ Q² / C
- Higher voltage or charge increases the stored energy.
Capacitors in Series and Parallel
- Parallel: total capacitance Cₜ = C₁ + C₂ + ..., voltage across all is the same.
- Series: 1/Cₜ = 1/C₁ + 1/C₂ + ..., charge on each is the same, total voltage divides.
- In series, total capacitance is less than the smallest individual capacitor.
- Combination circuits require stepwise calculation.
Charge Redistribution
- When a charged capacitor connects to an uncharged one, charge redistributes proportionally to their capacitances.
- Total charge is conserved; shared voltage is found using Q_total = (C₁ + C₂)V.
- Some energy is lost as heat during redistribution.
Discharging Capacitors and Exponential Decay
- Capacitor discharge (current, voltage, charge) follows exponential decay, not a straight line.
- Discharge is described by:
- Q = Q₀e^(–t/RC)
- V = V₀e^(–t/RC)
- I = I₀e^(–t/RC)
- The time constant RC is the time for quantities to drop to 37% of initial values.
- Larger R or C results in slower discharge.
Key Terms & Definitions
- Capacitance (C) — charge stored per unit voltage; unit: farad (F).
- Dielectric — insulating material between capacitor plates.
- Time constant (RC) — time for a discharging capacitor's values to fall to 37% of initial.
- Farad (F) — unit of capacitance; practical capacitors use μF or nF.
Action Items / Next Steps
- Practice solving circuit problems with capacitors in series and parallel.
- Review exponential decay calculations for capacitor discharge.
- Complete assigned homework or textbook readings on capacitor energy and applications.