Simplifying Circuits Label which resistors are in series

Simplifying Circuits

Label which resistors are in series and which are in parallel

Find Req (from A to B)

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

Example • Three nodes R 1 + - Vs + R 2 R 3 Is Vo -

Example • 5 Branches R 1 + - Vs + R 2 R 3 Is Vo -

Example • Three Loops, if starting at node A A + - B R 1 Vs + R 2 R 3 C Is Vo -

Kirchhoff’s Rule #1 • Junction Rule (aka Kirchhoff’s Current Law): Current into a junction equals the current out of a junction. • I 3=I 1+I 2

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

Example • Determine the currents through each resistor

Example • Find I 1, I 2 and I 3.