**Parallel Circuits Definition:**

Parallel Circuits Definition – The complex number system simplifies the analysis of parallel ac circuits. In series circuits, the current is the same in all parts of the series circuit. In parallel ac circuits, the voltage is the same across each element.

**Parallel RC Circuits:**

The voltages for an RC series circuit can be expressed using complex numbers, where the resistive voltage is the real part of the complex voltage and the capacitive voltage is the imaginary part. For parallel RC circuits, the voltage is the same across each component. Here the total current can be represented by a complex number. The real part of the complex current expression is the resistive current; the capacitive branch current is the imaginary part.

**Parallel RL Circuits:**

In a parallel RL circuit, the inductive current is imaginary and lies on the -j axis. The current angle is negative when the impedance angle is positive. Here also the total current can be represented by a complex number. The real part of the complex current expression is the resistive current; and inductive branch current is the imaginary part.

**Compound Circuits:**

In many cases, ac circuits to be analysed consist of a combination of series and parallel impedances. Circuits of this type are known as **series-parallel**, or **compound circuits**. Compound circuits can be simplified in the same manner as a series-parallel dc circuit consisting of pure resistances.