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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
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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 • 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
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
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 • DV = DPE • In a uniform electric field • DV = -EDd • Between a point at infinity and a point near a point charge • DV = kCq 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 DV • C = e0 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 k
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 QDV • PE = ½ C(DV)2