Illustration Parallel connection of three resistors and their current and voltage

Three electrical resistors \(R_1\), \(R_2\) and \(R_3\) are connected parallel (side by side). that is they are connected so that different current flows through all three. The total current \(I\) splits at the junctions so that current \(I_1\) flows through the first resistor, current \(I_2\) flows through the second resistor, and current \(I_3\) flows through the third resistor. This is the characteristic of a parallel connection of resistors!

For the current to flow at all, a voltage source is connected to the resistors, which supplies the voltage \(U\). The positive pole of the voltage source is connected to one end of all three resistors and the negative pole is connected to the other end of all three resistors.

When resistors are connected in parallel, the reciprocals of the individual resistances add up:\[ \frac{1}{R} ~=~ \frac{1}{R_1} ~+~ \frac{1}{R_2} ~+~ \frac{1}{R_3} \]where \(R\) is the total resistance of the series circuit. This is also called equivalent resistance.