Page 109 - Basic Electrical Engineering

2.3 SERIES–PARALLEL CIRCUITS

Resistances, capacitances, and inductances are often connected in series, in
parallel, or a combination of series and parallel. We need to calculate the

division of voltage and currents in such circuits

2.3.1 Series Circuits

When a number of resistances are connected end to end across a source of
supply, there will be only one path for the current to flow as shown in Fig.
2.9. The circuit is called a series circuit.

Figure 2.9 DC series circuit

The voltage drops across the resistances are V , V , V , and V ,
1
4
3
2
respectively. Since the same current is flowing through all the resistances, we
can write

V = IR , V = IR , V = IR , and V = IR 4
2
2
3
4
3
1
1
Again, the total voltage, V applied is equal to the sum of the voltage drops
across the resistances,
Thus we can write

V = V + V + V + V 4
2
3
1
To find the value of equivalent resistance of a number of resistances
connected in series, we equate the voltage, V of the two equivalent in units as

shown in Fig. 2.9 (a) and Fig. 2.9 (b) as