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Topic 4

Topic 4. The Kirchhoff Laws. (Sections 2.3 & 2.4). i 4. R 2. R 1. +. v 4. v s. R 4. R 3. -. We’d like to “solve” the circuit. That is we’d like to find out:. (a) the voltage drop across each resistor. For example. A Circuit.

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Topic 4

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  1. Topic 4 The Kirchhoff Laws (Sections 2.3 & 2.4) Kirchoff Laws

  2. i4 R2 R1 + v4 vs R4 R3 - We’d like to “solve” the circuit. That is we’d like to find out: (a) the voltage drop across each resistor For example A Circuit Here’s a circuit with one voltage source and several resistors Either will do since we can use Ohm’s Law to find the other or (b) the current that flows through it. To do that we need to know how voltages and currents combine Kirchoff Laws

  3. R2 R1 Tee Junction vs R4 R3 i1 i2 i3 i2 i1 i3 The Kirchhoff Current Law What goes in must come out Kirchoff Laws

  4. R2 R1 vs R4 R3 i1 i2 i3 i2 i1 i3 Effect of Reference Directions Arbitrarily changed current reference directions What goes in must come out or How many ways could we choose reference directions for this junction? Kirchoff Laws 8

  5. i2 i1 i3 i4 In General At any node (a node is a point where two or more elements meet) The sum of the incoming currents The sum of the outgoing currents = Kirchoff Laws

  6. i2 i1 i3 i4 Alternatively The sum of all currents (treating incoming currents as positive and outgoing currents as negative) is zero Kirchoff Laws

  7. R2 R1 vs R4 R3 2 3 1 c a b 0 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. There are 3 loops There are 4 nodes in the circuit below Kirchoff Laws

  8. R2 R1 vs R4 R3 v1 v2 + - - + c + + v4 v3 a b - - Kirchhoff Voltage Law The algebraic sum of all voltages around any closed path (loop) in a circuit is zero We need to assign some voltages …but which way is uphill and which is downhill? Take your best shot …and let the algebra sort it out. Loop a Loop b Loop c Kirchoff Laws

  9. vo vB Ri io vi - + io + By KVL: Ri Solving for vo: vo vB Applying Ohm’s Law: - Improved Model for a Battery Voltage drops as current increases Internal Resistance Kirchoff Laws

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