In this presentation a two-loop circuit is analyzed:• animation is used to demonstrate choosing current direction and generating

resistor polarities• Creating a junction point equation• the idea of generating loop equations by “walking the loop” is demonstrated via

an animated “robot cockroach voltmeter.”

Simply click through the slides and provide your own narration

Kirchhoff

Junction Points and Loop WalksBy Leo Takahashi, The Pennsylvania

State University, Beaver Campus

A circuit is constructed with known

battery emfs (દ1 and દ2) and known

resistances (R1, R2, and R3); we wish

to know the values of the currents.

We will use Kirchhoff’s Rules as follows:

At a JUNCTION POINT the currents in must equal the currents out.

Around any CLOSED LOOP the sum of the potential differences (voltages) must equal zero.

V

દ1 દ2

R1

R2

R3

I1

I2

I3

a

b

At a: I1 = I2 + I3

V

+ +

- -

+ -

+

-

+ -

= 0

- I1R1

- I2R2

V

+ I2R2

- દ2

- I3R3

= 0

+દ1

Loop 1 Loop 2

These three equations

I1 = I2 + I3

દ1 – I1R1 – I2R2 = 0

I2R2 – દ2 – I3R3 = 0can be solved for the three

unknown currents.