Capacitance

Capacitors A capacitor is a device used to store energy using charges and electric field. They are a number of uses for capacitors in our modern world: Pulsed Lasers/Weapons Help engines run Touch screens (like this SMARTboard) Filters for electrical circuits Capacitors work using the physics of capacitance.

Capacitance Capacitance – the ratio of charges on a conductive plate to the voltage between the conductive plates. Capacitance is like Capacity The Capacity of a milk carton is the volume it holds Heat Capacity is the amount of energy an object can store without an increase in temp.

Capacitance Basic capacitance equation: Capacitance of different objects: Isolated sphere 𝐶=4𝜋 𝜀 𝑜 𝑟 Parallel Plates 𝐶= 𝜀 𝑜 𝐴 𝑑 Charge on Plate Capacitance 𝐶= 𝑄 ∆𝑉 Potential Difference (Voltage) Radius 8.854 x 10-12 C2/Nm2 Area Separation Unit: Farad Scalar Quantity

Capacitance Since charges are being held in place there is also potential energy that is being stored (which can then be turned into kinetic energy of the moving electrons!) 𝑃𝐸= 1 2 𝐶 ∆𝑉 2

How a Capacitor Works Parallel Plate Capacitor We can change the capacitance by affecting the area of the plates, the distance between the plates, or the voltage of the battery. Electrons move from the plate leaving it positively charged + - Electrons build up on the plate leaving it negatively charged Electric Field in Wire Electric Field in Wire + Battery -

Parallel Plate Capacitors The separation between the two charged plates creates potential energy. The potential energy comes from the chemically stored potential energy in the battery. 𝑃𝐸= 1 2 𝐶 𝑉 2 𝐸= ∆𝑉 𝑑 - +

Dielectrics One way to increase the capacitance of a parallel plate capacitor is to insert an insulator (like glass) between the two conductive plates. This insulator is called a dielectric.

Dielectric cont. This slightly changes our equation for a parallel plate capacitor to look like this: 𝐶=𝜅 𝐶 𝑜 𝐶=𝜅 𝜀 𝑜 𝐴 𝑑 Capacitor with dielectric Capacitor without dielectric Dielectric Constant

Combinations of Capacitors Basic Circuit Symbols Wire Capacitor Battery Switch

Capacitors in Parallel Parallel Circuits are ‘stacked like pancakes.’ C1 C2 C3 Battery

Parallel Circuits Parallel Circuits have two important characteristics: The Current varies over each component in the circuit: 𝐼 𝑡𝑜𝑡𝑎𝑙 = 𝐼 1 + 𝐼 2 + 𝐼 3 The Voltage stays constant over each component in the circuit: ∆𝑉 𝑡𝑜𝑡𝑎𝑙 = ∆𝑉 1 = ∆𝑉 2 = ∆𝑉 3

Capacitors in Parallel To find the equivalent capacitance (a single capacitor to replace all of the capacitors), we use the following equation: 𝐶 𝐸𝑄𝑈𝐼𝑉 = 𝐶 1 + 𝐶 2 + 𝐶 3 C1 C2 CEQUIV C3 Battery Battery

Capacitors in Series Series Circuits are placed next to each other. C1 Battery

Series Circuits Series Circuits have two important characteristics: The Current stays constant over each component in the circuit: 𝐼 𝑡𝑜𝑡𝑎𝑙 = 𝐼 1 = 𝐼 2 = 𝐼 3 The Voltage varies over each component in the circuit: ∆𝑉 𝑡𝑜𝑡𝑎𝑙 = ∆𝑉 1 + ∆𝑉 2 + ∆𝑉 3

Capacitors in Series To find the equivalent capacitance (a single capacitor to replace all of the capacitors), we use the following equation: 1 𝐶 𝐸𝑄𝑈𝐼𝑉 = 1 𝐶 1 + 1 𝐶 2 + 1 𝐶 3 C1 C2 C3 CEQUIV Battery

Practice Problem What is the potential difference between the plates of a 3.3 F capacitor that stores sufficient energy to operate a 75 W light bulb for 30 seconds? Remember: Power = 𝐸𝑛𝑒𝑟𝑔𝑦 𝑇𝑖𝑚𝑒