# Series and Parallel Networks

### Series Circuits

Figure 43.1 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 will flow and the p.d. across each resistor may be determined from the voltmeter readings V1 , V2 and V3

In a series circuit

(a) the current I is the same in all parts of the circuit and hence the same reading is found on each of the ammeters shown, and

(b) the sum of the voltages V1, V2 and V3 is equal to the total applied voltage, V, i.e.

V = V1 + V2 + V3

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

#### Potential Divider

The voltage distribution for the circuit shown in Figure 43.2(a) is given by:

The circuit shown in Figure 43.2(b) is often referred to as a potential divider circuit. Such a circuit can consist of a number of similar elements in series connected across a voltage source, voltages being taken from connections between the elements. Frequently the divider consists of two resistors as shown in Figure 43.2(b), where

For example, to determined the value of voltage V shown in Figure 43.3: Redrawing the circuit as shown in Figure 43.4

Parallel Networks

Figure 43.5 shows three resistors, R1, R2 and R3 connected across each other, i.e. in parallel, across a battery source of V volts.

Current Division

For the circuit shown in Figure 43.6,

Wiring Lamps in Series and in Parallel

##### Series connection

Figure 43.9 shows three lamps, each rated at 240 V, connected in series across a 240 V supply.

(i) Each lamp has only V across it and thus each lamp glows dimly.

(ii) If another lamp of similar rating is added in series with the other three lamps then each lamp now has V across it and each now glows even more dimly.

(iii) If a lamp is removed from the circuit or if a lamp develops a fault (i.e. an open circuit) or if the switch is opened, then the circuit is broken, no current flows, and the remaining lamps will not light up.

(iv) Less cable is required for a series connection than for a parallel one.

The series connection of lamps is usually limited to decorative lighting such as for Christmas tree lights.

##### Parallel connection

Figure 43.10 shows three similar lamps, each rated at 240 V, connected in parallel across a 240 V supply.

(i) Each lamp has 240 V across it and thus each will glow brilliantly at their rated voltage.

(ii) If any lamp is removed from the circuit or develops a fault (open circuit)

or a switch is opened, the remaining lamps are unaffected.

(iii) The addition of further similar lamps in parallel does not affect the bright- ness of the other lamps.

(iv) More cable is required for parallel connection than for a series one.

The parallel connection of lamps is the most widely used in electrical installations.