Lecture 15 Chapter 28 Circuits Review emf device label terminal at higher V as and lower V as Draw emf arrow from to terminal charge carriers move against E field in emf device from lower to higher V Review Kirchhoff s loop rule in traversing a circuit loop the sum of the changes in V is zero V 0 Resistance rule Move through resistor in direction of current V iR in opposite direction V iR Emf rule Move through emf device in direction of emf arrow V E in opposite direction V E Review Put real battery in circuit Using Kirchhoff s loop rule and starting at point a gives E ir iR 0 E i r R For ideal battery r 0 and we get same as before E iR Circuits 25 Arbitrarily label currents using different subscript for each branch Using conservation of charge can write iin iout At point d At point b i1 i3 i2 At point a i1 i1 i1 i3 i2 At point c i2 i2 Circuits 26 Kirchhoff s junction rule or current law From conservation of charge Sum of currents entering a junction is equal to sum of currents leaving that junction Kirchhoff s loop rule or voltage law From conservation of energy Sum of changes in potential going around a complete circuit loop equals zero Circuits 27 Resistors in series Have identical currents i through them Use Kirchhoff s loop rule E iR1 iR2 iR3 0 E i R1 R2 R3 Circuits 28 Resistors in series Replace 3 resistors with equivalent resistor Req E i R1 R2 R3 Req R1 R2 R3 Circuits 29 Resistors in series Resistors have identical currents i Sum of V s across resistors applied V Req is sum of all resistors n Req R j j 1 Circuits 30 Checkpoint 2 If R1 R2 R3 rank greatest first A current through resistors i is same for all tie B V across them V iR R1 R2 R3 Circuits 31 Resistors in parallel Have same V across them Arbitrarily choose direction for currents in each branch Write down current relation for each resistor V i1 R1 V i2 R2 V i3 R3 Circuits 32 Resistors in parallel Apply Kirchhoff s junction rule at point a i i1 i2 i3 Substitute current values 1 1 1 i V R3 R1 R 2 Circuits 33 Resistors in parallel Replace 3 resistors with equivalent resistor Req 1 1 1 1 R eq R1 R 2 R3 Circuits 34 Resistors Series R eq Capacitors Series n n R j 1 j Parallel 1 1 Ceq j 1 C j Parallel n 1 1 Req j 1 R j C eq n C j 1 j Circuits 35 Checkpoint 4 Battery with potential V supplies current i to 2 identical resistors What is V across and i through either of the resistors if they are connected in A Series What is constant i is same V1 V 2 V iR B Parallel What is constant V is same i1 i 2 Circuits 36 What is i of the circuit Use Kirchhoff s loop rule Clockwise from point a gives E2 ir2 iR ir1 E1 0 Counterclockwise from point a gives E1 ir1 iR ir2 E2 0 Circuits 37 Solve for i E1 ir1 iR ir2 E2 0 E1 E 2 i R r1 r2 E1 4 4V E2 2 1V r1 2 3 r2 1 8 R 5 5 i 0 2396A 240mA Circuits 38 What is V across battery 1 s teminals Sum potential differences from point b to point a Clockwise Vb ir1 E1 Va Counterclockwise Va Vb E1 ir1 Va Vb 3 84V Vb iR ir2 E2 Va Va Vb i R r2 E2 Circuits 39 Checkpoint 3 A real battery has 12V and r 2 Is the V across the terminals greater than less than or equal to 12V if the current in the battery is A from to terminal LESS THAN Va E ir Vb B from to GREATER THANV a C i 0 EQUAL TO 12V E ir Vb i
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