FUNDAMENTAL LAWS FOR CIRCUIT ANALYSIS

Ohm's law:

At a constant temperature, the electrical current (I) flowing through a fixed linear resistance (R) is directly proportional to the voltage (V) applied across it, and also inversely proportional to the resistance.

V=IR

Kirchoff's Current law: 

The algebraic sum of currents at a particular node is zero. In other words, the sum of currents entering a node is equal to the sum of currents leaving the node.

Kirchoff's Voltage law:

The algebraic sum of voltages in a closed loop is zero. In other words, voltage drop in a loop is equal to the voltage raise in the loop.

Voltage Division rule for resistors connected in series: 

A voltage source V and two resistors R1 and R2 are in series.

Volatge V1 through resistor R1 is:

V1=(R1*V)/(R1+R2)

Volatge V2 through resistor R2 is:

V2=(R2*V)/(R1+R2)

Current Division rule for resistors connected in parallel: 

A current source I and two resistors R1 and R2 are in parallel.

Current I1 through resistor R1 is:

I1=(R2*I)/(R1+R2)

Current I2 through resistor R2 is:

I2=(R1*V)/(R1+R2)

Equivalent Resistance for parallel resistors:

Two resistors R1 and R2 are in parallel. Their equivalent resistance R is:

R=(R1*R2)/(R1+R2)

Equivalent Resistance for series resistors:

Two resistors R1 and R2 are in series. Their equivalent resistance R is:

R=R1+R2

Reference:

Fundamentals of Electric Circuits (Fifth Edition) by Charles K Alexander and Matthews N O Sadiku