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:
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).