Week 3: Basic Laws (Current and Voltage Division)

                                     Voltage Division

The voltage division rule (voltage divider) is a simple rule which can be used in solving circuits to simplify the solution. Applying the voltage division rule can also solve simple circuits thoroughly 

Voltage Division Rule: The voltage is divided between two series resistors in direct

proportion to their resistance.

Example:

Solution:

the Ohm's law implies that
v1(t)=R1i(t) (I)
v2(t)=R2i(t) (II)

Applying KVL
−v(t)+v1(t)+v2(t)=0→v(t)=v1(t)+v2(t) .

v(t)=R1i(t)+R2i(t)=(R1+R2)i(t) .

Hence
i(t)=v(t)R1+R2 .

Substituting in I and II
v1(t)=R1v(t)R1+R2 ,
v2(t)=R2v(t)R1+R2 .

Consequently

v1(t)=R1R1+R2v(t) ,v

2(t)=R2R1+R  2v(t) .

                              CURRENT DIVISION 

Current Division

A Current Divsion circuit is a circuit in which the main current from the power source is divided up in the circuit and, thus, different amounts of current are allocated to different parts of the circuit.

Example:

Suppose that R1=2Ω , R2=4Ω , R3=1Ω , IS=5A and VS=4V 

Solution:

IR2=R3R2+R3×IS=11+4×5=1A 
IR3=R2R2+R3×IS=41+4×5=4A .

IR1=IS=5A .

KCV around the loop assuming the positive terminal of the current source to be the one at bottom:
+VIS−R3×IR3−R1×IR1−VS=0
VIS=R3×IR3+R1×IR1+VS 
VIS=1×4+2×5+4=18V

Learnings: