Monday, December 2, 2013

Parallel Resistors

Parallel Resistors
Two resistors or any two devices are said to be in parallel when the same voltage physically appears across the two resistors
Equation of Parallel Resistors:
 
1 / R total = 1 / R1 + 1 / R2 + 1 / R3 +................
 
 
Note that we have defined the voltage across both resistor (Vp) and the current that flows through each resistor (Ia and Ib) and a voltage variable, Vp, for the voltage that appears across the parallel combination.
·    The voltage across the two resistors is the same.
·    The current through the parallel 
 combination is given by:
Ip= Ia + Ib
Ohm's Law gives the currents through the two resistors:
Ia = Vp /Ra
Ib = Vp /Rb
We can combine all of these relations, and when we do that, we find the following.
Ip= Ia + Ib
Ip= Vp /Ra + Vp /Rb
Ip= Vp[ 1/Ra + 1/Rb]
Ip= Vp/Rparallel

Example

Find the total resistance, RT of the following resistors connected in a parallel network.

 

The total resistance RT across the two terminals A and B is calculated as:

 

 

 


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