Lecture 12Chapter 26Capacitance - ExamplesCapacitance – Question #4 • A) In (a) are C1and C3in series?YES• B) In (a) are C1and C2in parallel?YES• Rank the Ceqof the 4 circuits.All the sameCapacitance – Question #9• After switches close for which circuit will the charge on the left-hand capacitor • A) increase?2• B) decrease?3•C) same?1CVq =• Charge flows until the capacitors have the same potential, VLecture 12Chapter 27Current and ResistanceCurrent (1)• What happens when charges move?• Isolated conductor –– Random motion of conduction electrons in both directions so no net transport of charges– Same potential everywhere, no E field inside or on surface so no electric F on electrons• No current in isolated conductorCurrent (2)• What happens when charges move?• Adding a battery –– Bias flow of conduction electrons in one direction have net transport of charge– Not a single potential, have E field inside which exerts Fon electrons • Current in a conductor when attached to a batteryCurrent (3)• Amount of current, i equals amount of q that passes in t through an area ⊥ to the flow• If i doesn’t vary with time (called steady state) q is conserved, i is the same for all planes which pass through conductor– Orientation doesn’t matterdtdqi =Current (4)• SI unit for current is ampere• Current is a scalar• Use arrows to indicate charge flow along conductor• q is conserved so sCA 11 =210iii +=Current (5)• Convention: a current arrow is drawn in direction of + charge flow– Defined direction of current is opposite to direction of physical current (electrons are the moving charges)• Current arrows are not vectors• Bending or reorienting wires does not change210iii +=+-+-Current (6)• Checkpoint #1 – What is the magnitude and direction of the current, i , in the lower right-hand wire?• q is conserved To the rightoutinii =Aiin11= iAiout+= 3Ai 8=Current (7)• Total current through a surface can be defined as • Current density, J – flow of charge through a cross section • If i uniform and parallel to dA• SI unit for J is A/m2∫•= AdJirr∫== JAJdAiAiJ =Current (8)• Represent J by streamlines• q is conserved so amount of i cannot change• J becomes greater in narrower conductor• Streamlines closer together mean greater J AiJ =Current (9)• No current in conductor electrons move randomly with speeds ≈ 106m/s• If current present electrons also move with a drift speed vd• Drift speeds are tiny vd≈ 10-5or 10-4m/s• Why do the lights come on quickly?• E field moves at speed of
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