Circuits Exclusives 2013: Series & Parallel Circuits

Components of an electrical circuit or electronic circuit can be connected in many different ways. The two simplest of these are called series and parallel and occur very frequently.

SERIES CIRCUIT:

In a series circuit, the current through each of the components is the same, and the voltage across the circuit is the sum of the voltages across each component. In a parallel circuit, the voltage across each of the components is the same, and the total current is the sum of the currents through each component.

In my experience and observation, Series Circuits are the simplest to work with.Here we have three resistors of different resistances. They share a single connection point. When added together the total resistance is 90-Ohms.

Current

$I = I_1 = I_2 = \dots = I_n$

In a series circuit the current is the same for all elements.

Resistors

The total resistance of resistors in series is equal to the sum of their individual resistances:

$R_\mathrm{total} = R_1 + R_2 + \cdots + R_n$

Inductors

Inductors follow the same law, in that the total inductance of non-coupled inductors in series is equal to the sum of their individual inductances:

$L_\mathrm{total} = L_1 + L_2 + \cdots + L_n$

Capacitors

Capacitors follow the same law using the reciprocals. The total capacitance of capacitors in series is equal to the reciprocal of the sum of the reciprocals of their individual capacitances:

$\frac{1}{C_\mathrm{total}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots + \frac{1}{C_n}$ .

PARALLEL CIRCUIT

If two or more components are connected in parallel they have the same potential difference (voltage) across their ends. The potential differences across the components are the same in magnitude, and they also have identical polarities. The same voltage is applicable to all circuit components connected in parallel. The total current is the sum of the currents through the individual components.

A parallel circuit is shown here and it has TWO common connection points with another component. In this case another resistor. We cannot add the values of each resistor together like we can in the previous series circuit. So what do we need to do?