Capacitance and Capacitors Section 11.3

Capacitors An arrangement of 2 parallel conducting plates that are separated by an insulator. In the diagram to the right, the plates are uncharged and are in a circuit supplied with emf, E. What will happen when we close the switch?

Charging a capacitor When the switch is closed, the emf causes movement of the electrons within the circuit, creating a positively charged plate on the side of the capacitor nearest the positive terminal, and a negatively charged plate on the side of the capacitor nearest the negative terminal. During charging, the potential difference across the space between the plates is less than the overall emf available to the circuit.

Charging a capacitor When the potential difference measured between the plates is equal in magnitude to the emf supplied by the source, then the capacitor is considered fully charged. Maximum potential difference, V, between the plates is equal to the emf, E, supplied to the system.

Graphically showing charging a capacitor Charging a capacitor: requires some source of eMF in the circuit Adding a resistor increases the time required to charge the capacitor to maximum capacity Capacitor charges more quickly at the beginning; as charge is accumulated on the plates, it is harder and harder to add more electrons to the negative plate

Graphically showing discharge of a capacitor Discharging requires a complete circuit that bypasses the source of eMF (essentially, short out the cell) Capacitor will discharge in a way that creates a current opposite to the direction created when charging Exponential decay; faster discharge at the beginning, eventually reaching 0.

Quantifying Capacitance Capacitance: The ratio of the charge stored on the plates to the potential difference between the plates. Unit = Coulomb per Volt C·V-1 = F (farad)

Graphing Capacitance As charge is added to a capacitor, the potential difference between the plates changes If we were to look at the total charge that is placed on a capacitor at different potential differences, what would the graph look like? (Potential vs Charge) What does the slope represent? What does the area under the line represent?

Energy stored in a capacitor Potential difference is equivalent to the energy, per unit charge, that is stored on the capacitor The area under a V-Q graph is equal to the energy stored 𝑬 𝒄𝒂𝒑𝒂𝒄𝒊𝒕𝒐𝒓 = 𝟏 𝟐 𝑸𝑽 OR: 𝑬= 𝟏 𝟐 𝑪 𝑽 𝟐

Determining capacitance from the size of the capacitor: For a pair of parallel plates: 𝑄 𝐴 = 𝜀 0 𝑉 𝑑 Q = charge stored A = area in which the plates overlap and are parallel d = separation distance between the plates V = potential difference between the plates e = permittivity constant of the insulator between the plates Rearrange and you get: 𝑪=𝜺 𝑨 𝒅

Dielectrics A dielectric material is an electrical insulator that becomes polarized when in the presence of an electric field The dielectric enhances the capacitance by decreasing the potential difference between the capacitor plates (by reducing the strength of the electric field between the plates) (read pages 459-460 for more detail)

Common dielectric constants The numbers in the table to the right (from your textbook) are equivalent to the ratio of the permittivity of the material to that of a vacuum Known as the “Dielectric Constant” or “Relative Permittivity”

Practice In a laboratory experiment, two parallel plates, each of area 100. cm2, are separated by 1.50 cm. Calculate the capacitance of the arrangement if the gap between the plates is filled with: Air Polystyrene

Time constant for a capacitor Time constant is the product between the resistance of a capacitor circuit and the capacitance: 𝜏 = RC

Capacitors in Series

Capacitors in parallel