Capacitors store electric charge and electrical potential energy in an electric field. This reference helps students connect the physical structure of a capacitor to the equations used in circuit problems. It is useful for reviewing charge, voltage, capacitance, energy storage, and dielectric materials before tests or labs.
Key Facts
- Capacitance is defined by , where is charge and is potential difference.
- The SI unit of capacitance is the farad, with .
- For a parallel-plate capacitor, , where is plate area, is plate separation, and is the dielectric constant.
- The electric field between ideal parallel plates is approximately .
- The energy stored in a capacitor can be written as .
- Capacitors in parallel have equivalent capacitance and share the same voltage.
- Capacitors in series satisfy and carry the same charge.
- Adding a dielectric increases capacitance by the factor , so for the same geometry.
Vocabulary
- Capacitor
- A device that stores separated electric charge and electric potential energy in an electric field.
- Capacitance
- The ratio of stored charge to potential difference, given by .
- Dielectric
- An insulating material placed between capacitor plates that increases capacitance and reduces the effective electric field.
- Equivalent capacitance
- The single capacitance value that can replace a network of capacitors while producing the same overall circuit behavior.
- Potential difference
- The voltage between two points, equal to the electric potential energy change per unit charge.
- Stored energy
- The energy held in a capacitor's electric field, often calculated with .
Common Mistakes to Avoid
- Using resistor rules for capacitor combinations is wrong because capacitors add directly in parallel and reciprocally in series.
- Assuming charge is the same on parallel capacitors is wrong because parallel capacitors share the same voltage, while charge depends on .
- Assuming voltage is the same on series capacitors is wrong because series capacitors carry the same charge and the voltage divides according to .
- Forgetting to square the voltage in is wrong because capacitor energy depends quadratically on potential difference.
- Ignoring unit conversions is wrong because values like and must be converted before using SI formulas.
Practice Questions
- 1 A capacitor is connected to a battery. What charge is stored on the capacitor?
- 2 Two capacitors, and , are connected in parallel. What is ?
- 3 A capacitor stores of energy. What voltage is across it?
- 4 A dielectric is inserted between the plates of an isolated charged capacitor. Explain what happens to the capacitance, voltage, and stored energy.
Understanding Capacitors & Capacitance Reference
When a capacitor is connected to a battery, electrons move through the wires onto one conducting plate. Electrons leave the other plate, making it positively charged. The insulating gap prevents charge from crossing directly between the plates.
Instead, the separated charges create an electric field across the gap. At first, charge moves quickly because the voltage across the capacitor is small. As more charge builds up, the capacitor's voltage rises and opposes further movement of charge from the battery.
In a simple direct current circuit, the charging current eventually becomes nearly zero. Real capacitors are not perfect, so a tiny leakage current may still pass through the insulating material.
The shape and material of a capacitor control how much charge can be separated without producing too large a voltage. Larger plates give more surface for opposite charges to face each other. A smaller gap makes the electric field stronger for a given voltage, so the same amount of charge produces a larger effect.
A dielectric works because its molecules shift slightly in the electric field. This polarization creates bound charges near the plates. Their field partly opposes the original field.
If the capacitor stays connected to a battery, more charge flows onto the plates until the original voltage is restored. If it is disconnected first, inserting a dielectric lowers the voltage instead. Keeping track of whether a battery remains connected is essential in these problems.
Circuit arrangements are easier to understand by following conductors and connection points. Capacitors joined across the same two points have the same voltage because each plate pair is connected to the same locations in the circuit. Their ability to hold charge combines because the battery can place charge on every capacitor.
In a series chain, the middle conductors cannot gain net charge if they started neutral. This forces each capacitor to have equal charge magnitude. The voltage is then shared between them.
A capacitor with a smaller capacitance takes a larger share of the total voltage. This matters in real circuits because a small capacitor may exceed its voltage rating first. The total capacitance of a series chain is smaller than the smallest individual capacitance.
Stored energy is located in the electric field, especially in the space between plates. The energy rises rapidly as voltage rises, which is why high voltage capacitors can be dangerous even when disconnected from a power source. A charging circuit with a resistor takes time to settle.
Its time constant equals resistance times capacitance. After one time constant, the capacitor is substantially charged, though not completely charged. This behavior is used for camera flashes, timing circuits, power supply smoothing, touch sensors, and memory backup.
In calculations, watch unit prefixes closely. Microfarads, nanofarads, and picofarads differ by large factors.
In labs, observe capacitor polarity because many electrolytic capacitors can be damaged by reverse connection. Discharge a capacitor safely through a suitable resistor before handling it.