Series and Parallel Circuits

Series Circuits

The figure below shows three resistors R₁, R₂, and R₃ connected end to end i.e. in series with a battery source of V volts.

Since the circuit is closed, a current I flow and the voltage across each resistor may be determined from the voltmeter readings V₁, V₂, and V₃.

In a series circuit:

• The current I is the same in all parts of the circuit; therefore the same reading is found on each of the two ammeters represented by (A).
• The sum of the voltage V₁, V₂, and V₃ is equal to the total applied voltage V i.e.

Thus, for a series circuit, the total resistance is obtained by adding together the values of the separate resistances.

Potential Divider

Consider the circuit below:

The voltage distribution in the above circuit is given by:

The circuit below is normally referred to as a potential divider circuit.

This kind of circuit shown above can consist of a number of similar elements in series connected across a voltage source, voltages being taken from connections between elements. In most cases the divider consists of two resistors as shown in the circuit above; where:

A potential divider is the simplest way of producing a source of lower e.m.f. from a source of higher e.m.f. and this is the basic operating mechanism of the potentiometer, a measuring device for accurately measuring potential differences.

You can also read: Basic electric circuits

Parallel Circuits

Let’s consider the circuit below:

The resistors R₁, R₂, and R₃ in the above circuit are connected across each other i.e. in parallel, across a battery source of V volts.

In a parallel circuit:

• The sum of the currents I₁, I₂ and I₃ is equal to the total circuit current I, i.e.

 I = I₁ + I₂ + I₃

• The source voltage V volts, is the same across each of the resistors.

Current Division

Let’s consider the circuit below:

From the circuit above, the total circuit resistance R_T is given by:

Relative and Absolute Voltages in Electrical Circuits

In an electrical circuit, the voltage at any point can be quoted as being ‘’with reference to” (w.r.t.) any other point in the circuit.

Considering the circuit below:

If a voltage at a point A is quoted with reference to point B, then the voltage is written as V_AB. This is known as a relative voltage. In the circuit above, the voltage at A w.r.t. B is 2 x 40 = 80 V and written as V_AB = 80 V.

We must also indicate whether the voltage at A w.r.t. B is closer to positive terminal or the negative terminal of the supply source. Point A is nearer to the positive terminal than B so is written as V_AB = 80 V or V_AB = +80 V or V_AB = 80 V +ve.

If the voltage at B w.r.t. A is required, then V_BA is negative and is written as V_BA = -80 V or V_BA = 80 V –ve.

If the reference point is changed to the earth point, then any voltage taken w.r.t. the earth is known as an absolute potential. If the absolute voltage of A is required, then this will be the sum of the voltages across the 40 ꭥ and 5 ꭥ resistors i.e. (40×2) + (5×2) = 90 V and is written as V_A = 90 V or V_A = 90 V +ve, positive since moving from earth point to point A is moving towards positive terminal of the source. If the voltage is negative w.r.t. earth then this must be indicated e.g. V_C = 20 V negative w.r.t. earth and is written as V_C = -20 V or V_C = 20 V –ve.