Resistors in parallel , Physics

Resistor in Parallel 

Components are said to be in parallel when they are connected in such a way as to provide alternative paths for current flow.

1869_resistor in parallel.png

The characteristics of such a parallel combination are:

  • The voltage across each component is the same.
  • The current through each component is determined by the resistance of that component
  • Ohm's law applies to each component connected in parallel.

In the diagram below.         V1 = V2 = V3 = V


and                                        I = I1 + I2 + I3   (by Kirchoff's first law) 

307_resistor in parallel1.png

From Ohm's law      I = V/R   

 

Therefore     2190_resistor in parallel2.png

and  465_resistor in parallel3.png

Hence the three resistors shown above may be replaced by a single resistor of value RTOTAL which may be computed using the above equation.  Note that the most usual error which occurs when using this equation is to forget that the calculation on the right hand side of the equation gives the reciprocal of the equivalent resistance 1\RTOTAL and therefore needs inverting to find RTOTAL.       


To avoid this possible error the equation may be remembered in the form:

 

2304_resistor in parallel4.png

Having found RTOTAL it is now possible to use Ohm's law to calculate either V or I, providing one of the two is known.  Knowing V (= V1 = V2 = V3 etc) it is now possible to find the current values through the branches I1, I2, I3­ etc (provided of course that R1, R2, R3 etc are known).

  • As a check, the total resistance of any parallel combination of resistors should always be less than the value of the lowest resistor in the network.
Posted Date: 9/13/2012 3:33:28 AM | Location : United States







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