Electrical Energy and Capacitance

Electrical Potential Energy Potential energy associated with the electrical force between two charges Form of mechanical energy When charge moves  work is done If electric field applies a force to a charge  potential energy decreases If work is done to oppose the electric field  potential energy increases

Calculating Potential Energy  PE = -qE  d  If moving in the direction of the electric field PE increases if charge is negative PE decreases if charge is positive PE = -qEd –PE in a uniform electric field

Electric Potential Energy for a Pair of Charges PE = k C q 1 q 2 r Reference point is infinity –At infinity, PE goes to zero as r goes to infinity Positive work must be done to bring like charges together  PE is positive for like charges  PE is negative for unlike charges

Electric Potential Electrical potential energy associated with a charged particle in an electric field divided by the charge of the particle Mathematically expressed V=PE q

Potential Difference Change in electrical potential energy divided by the charge SI unit is the volt V = J/C  V =  PE In a uniform electric field  V = -E  d Between a point at infinity and a point near a point charge  V = k C q r

Batteries Potential difference maintained across terminals of battery For example –12 volt battery, positive terminal is 12V higher in potential than the negative terminal Battery does work on charge to move it from the negative to the positive terminal –Net result is electric potential increase of 12 V –Every coulomb of charge  12 J of PE

Capacitor Device that stores energy Parallel-plate capacitor –Plates connected to two terminals of battery –Charges removed from one plate to another One plate  net positive charge Other plate  equal net negative charge –Charge transfer stops when potential difference between the two plates is equal to the potential difference between the terminals of the battery

Calculating Capacitance C = Q  V C =  0 A d Unit is the Farad

Factors that Affect Capacitance Plate area –Capacitance increases as plate area increases Plate separation –Capacitance increases with decreasing plate separation Material between the plates –Dielectric – insulating material –Inserting a dielectric increases capacitance by the dielectric constant 

Discharge of a Capacitor Capacitor remains charged until connected to conducting material Once connected  discharge Charges move back from one plate to another until both plates are uncharged –State of lowest potential energy

Energy and Capacitors Work is done to move charges to opposite plate of capacitor –Stores electrical potential energy PE = ½ Q  V PE = ½ C(  V) 2