1. Engineering 1333: Electrical Circuits 9/16/20059/12/2007Kirchoff Laws1 Topic 4 The Kirchhoff Laws (Sections 2.3 & 2.4)

2. 9/16/2005Kirchoff Laws 2 A Circuit R1R1 R2R2 R3R3 R4R4 vsvs Here’s a circuit with one voltage source and several resistors We’d like to “solve” the circuit. That is we’d like to find out: (a) the voltage drop across each resistor (b) the current that flows through it. or Either will do since we can use Ohm’s Law to find the other For example v4v4 + - i4i4 To do that we need to know how voltages and currents combine

3. 9/16/2005Kirchoff Laws 3 The Kirchhoff Current Law R1R1 R2R2 R3R3 R4R4 vsvs i1i1 i3i3 i2i2 Tee Junction i1i1 i2i2 i3i3 What goes in must come out

4. 9/16/2005Kirchoff Laws 4 Effect of Reference Directions R1R1 R2R2 R3R3 R4R4 vsvs i1i1 i3i3 i2i2 i1i1 i2i2 i3i3 What goes in must come out Arbitrarily changed current reference directions How many ways could we choose reference directions for this junction? 8 or

5. 9/16/2005Kirchoff Laws 5 In General At any node The sum of the incoming currents The sum of the outgoing currents = (a node is a point where two or more elements meet) i2i2 i1i1 i3i3 i4i4

6. 9/16/2005Kirchoff Laws 6 Alternatively i2i2 i1i1 i3i3 i4i4 The sum of all currents (treating incoming currents as positive and outgoing currents as negative) is zero

7. 9/16/2005Kirchoff Laws 7 A Loop Start at any node trace a closed path through the circuit coming back to the original node without passing through any intermediate node more than once. R1R1 R2R2 R3R3 R4R4 vsvs 0 1 2 3 a b There are 4 nodes in the circuit below There are 3 loops c

8. 9/16/2005Kirchoff Laws 8 Kirchhoff Voltage Law The algebraic sum of all voltages around any closed path (loop) in a circuit is zero R1R1 R2R2 R3R3 R4R4 vsvs …but which way is uphill and which is downhill? We need to assign some voltages v4v4 v1v1 v2v2 v3v3 + - - - - + + + Take your best shot …and let the algebra sort it out. a b c Loop c Loop b Loop a

9. 9/16/2005Kirchoff Laws 9 Improved Model for a Battery vovo ioio vBvB Voltage drops as current increases vBvB vovo ioio RiRi + - RiRi Internal Resistance vivi + - By KVL: Solving for v o : Applying Ohm’s Law: