Kirchoff’s Rules

Purpose: solve complex circuits

Some terminology• Loop: ANY closed

path in a circuit. This one has three loops.

The loop direction is arbitrary.

Best practice: follow out of the + side of battery when possible.

Junction: where two or more wires meet.

5 Ω 12 V

10 Ω

6 V 20 Ω

Purpose of Rules:

• Since some circuits are too complex they must be solved using Kirchoff’s Rules.

These rules follow the principle and ideals of conservation of charge and conservation of energy.

The rules help keep track of +/- for potentials.

Before applying rules, label currents in loops

Choose current directions. Use arrows right on the wire to indicate current and label with I1 I2, and/or I3.

Cannot have all three currents enter or leave a junction simultaneously. At least one direction must be different coming in or out of a junction.

5 Ω 12 V

10 Ω

6 V 20 Ω

1. Junction Rule

• At any junction the sum of all currents entering must equal the sum of all currents leaving the junction.

This is conservation

Of charge.

Equations:

5 Ω 12 V

10 Ω

6 V 20 Ω

Loop Rule

• The sum of the changes in potential around any closed path of a circuit must be zero.

This is conservation of energy.

5 Ω 12 V

10 Ω

6 V 20 Ω

Voltage: + or - ???

• When tracing a current

through a loop, start at

a battery.

The V will be + when you

trace neg to pos. (uphill)

The V will be – when you trace pos to neg. (downhill)

5 Ω 12 V

10 Ω

6 V 20 Ω

IR values through resistors

• Apply Ohms Law:

V = IR

IR will be neg when

direction of loop and current match.

IR will be pos when loop trace goes against current

5 Ω 12 V

10 Ω

6 V 20 Ω

The idea is to get all the equations and the correct signs

• Apply junction rule for current equation

• Apply loop rule and sign protocol for IR and battery voltages

5 Ω 12 V

10 Ω

6 V 20 Ω