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.

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) 

From Ohm's law      I = V/R   

Therefore     

and  

Hence the three resistors shown above may be replaced by a single resistor of value R_TOTAL 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\R_TOTAL and therefore needs inverting to find R_TOTAL.       

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

Having found R_TOTAL 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.