Electrical Energy and Capacitance

1. Electrical Energy and Capacitance

2. 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

3. Calculating Potential Energy • DPE = -qEDd • 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

4. Electric Potential Energy for a Pair of Charges • PE = kCq1q2 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

5. 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

6. Potential Difference • Change in electrical potential energy divided by the charge • SI unit is the volt V = J/C • DV = DPE • In a uniform electric field • DV = -EDd • Between a point at infinity and a point near a point charge • DV = kCq r

7. 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

8. 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

10. Calculating Capacitance • C = Q DV • C = e0 A d • Unit is the Farad

11. 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 k

12. 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

13. Energy and Capacitors • Work is done to move charges to opposite plate of capacitor • Stores electrical potential energy • PE = ½ QDV • PE = ½ C(DV)2