# 4.07 Resistors in parallel.

## Parallel circuits.

• If several branches are connected in parallel the voltage across each branch is the same.
The top ends of all three resistors are connected to the same potential and the bottom ends are also connected to a common potential, so the potential difference across each must be the same. Using the analogy we used in the section on Kirchoff's voltage law: Its similar to three staircases each running from the top of a building to the bottom, obviously in this example the difference in height between the top and bottom of each staircase will be the same.
• As we have already seen from Kirchhoff's current law, the sum of the current entering a junction is equal to the sum of current leaving the junction.

## Resistors in parallel.

The diagram below shows three resistors connected in parallel. To show how to calculate the total resistance, we will use Kirchhoff's current law and ohms law. According to Kirchoff's current law, the sum of the currents flowing out of the junction (and through each resistor), is equal to the current flowing into the junction.

• IT = I1 + I2 + I3.

According to Ohm's law,    I = V/R.     Therefore substituting for I gives;

• V/RT = V/R1 + V/R2 + V/R3.
(RT is the total resistance and V is the common voltage across each resistor).

dividing both sides of the equation by V, gives;

• 1/RT = 1/R1 + 1/R2 + 1/R3.

Therefore to calculate the total resistance of resistors in parallel;
1/RT = 1/R1+ 1/R2 + 1/R3.