RESISTORS IN PARALLEL
Resistors can be connected such that they branch out from a single point (known as a node), and join up again somewhere else in the ciruit. This is known as a parallel connection. Each of the three resistors in Figure 1 is another path for current to travel between points A and B.
Figure 1 Example of a circuit containing three resistors connected in parallel
Figure2 Circuit containing resistors in parallel, equivalent to Figure 1
Note that the node does not have to physically be a single point; as long as the current has several alternate paths to follow, then that part of the circuit is considered to be parallel. Figures 1 and 2 are identical circuits, but with different appearances.
At A the potential must be the same for each resistor. Similarly, at B the potential must also be the same for each resistor. So, between points A and B, the potential difference is the same. That is, each of the three resistors in the parallel circuit must have the same voltage.
Also, the current splits as it travels from A to B. So, the sum of the currents through the three branches is the same as the current at A and at B (where the currents from the branch reunite).
By Ohm's Law, equation  is equivalent to:
By equation , we see that all the voltages are equal. So the V's cancel out, and we are left with
This result can be generalized to any number of resistors connected in parallel.
Since resistance is the reciprocal of conductance, equation  can be expressed in terms of conductances.