Kirchoff's Junction Rule

The sum of the currents flowing into a junction is equal to the sum of the currents flowing out of said junction.

Mathematically,

$I_in=I_out$

Diagrammatically,

Kirchoff's Loop Rule

For any closed loop,the sum of the voltage lifts is equal to the sum of voltage drops.

Mathematically,

$$V_(net)=0$$

Diagrammatically,

LR(A):Vs-Vr=0

Conventions For Kirchoff's Law

• If we travel through a battery (while summing voltages) from low to high (negative to positive) the voltage is positive;high to low voltage is negative.
• If we follow current through a resisitor then,V=-IR;If we oppose current through a resistor then V=IR
• Loops and current directions are assigned arbitrarly with no preference in direction.
• Typically we will use one more loop than the number of junctions