1. Simplifying Circuits

2. Label which resistors are in series and which are in parallel

3. Find Req (from A to B)

4. Circuit Definitions
Node – any point where 2 or more circuit elements are connected together
Wires usually have negligible resistance
Any two points within the node has the same voltage
Branch – a circuit element between two nodes
Loop – a collection of branches that form a closed path returning to the same node without going through any other nodes or branches twice

5. Example
Three nodes R1 + Vo - Is + - Vs R2 R3

6. Example
5 Branches R1 + Vo - Is + - Vs R2 R3

7. Example A B C Three Loops, if starting at node A R1 + Vo - Is + - Vs

8. Kirchhoff’s Rule #1
Junction Rule (aka Kirchhoff’s Current Law): Current into a junction equals the current out of a junction.
I3=I1+I2

9. Kirchhoff’s Rule #2
Loop Rule (aka Kirchhoff’s Voltage Law): The voltage around a loop adds to 0.
Draw direction of each current through each circuit element (educated guess)
Draw a closed loop
Voltage from a battery is positive if going up a battery from negative to positive
Voltage from battery is negative if going down a battery from positive to negative
Voltage dropped by resistor is negative if the loop is in the same direction as the direction of the drawn current
Voltage dropped by resistor is positive if the loop is in the opposite direction as the direction of the drawn current

10. Example
Determine the currents through each resistor

11. Example
Find I1, I2 and I3.