The following points highlight the two main types of arrangement of resistance for conductors. The arrangements are: 1. Resistances in Series 2. Resistances in Parallel.
Type # 1. Resistances in Series:
When two or more conductors or coils or electrical appliances or resistors are joined together one after another to form a single circuit, they are said to be in series.
The effects of this series connection are as follows:
(i) Total resistance of the circuit is equal to algebraic sum of individual resistances connected in series.
ADVERTISEMENTS:
Three resistances R1, R2 & R3 shown in figure 4, are joined in series. If R be the total resistance of the circuit, then,
R = R1+ R2+ R3
(ii) All the resistances connected in series will carry the same current. In figure 4 three resistances carry the same current I.
ADVERTISEMENTS:
(iii) Voltage across each resistance is given by that resistance multiplied by the current flowing through the circuit. In figure 4,
V1 = IR1;
V2 = IR2;
V3 = IR3.
ADVERTISEMENTS:
(iv) Voltage applied across the circuit is equal to algebraic sum of voltages across individual resistors. In figure 4,
V = V1 + V2 + V3 = IR1 + IR2 + IR3 = I(R1 + R2 + R3) = IR
Type # 2. Resistances in Parallel:
When similar terminals of two or more conductors or coils or electrical appliances or resistors are joined together as shown in figure 5, they are said to be in parallel. Here each individual resistor forms an independent circuit.
Effects of parallel connection are as follows:
ADVERTISEMENTS:
(i) The reciprocal of equivalent resistance of the parallel combination is equal to algebraic sum of reciprocals of individual resistances connected in parallel.
Three resistances R1, R2 & R3 are joined in parallel as shown in fig. 5.
If R be the equivalent resistance of this parallel combination, then:
1/R = 1/R1 + 1/R2 + 1/R3.
ADVERTISEMENTS:
(ii) Total current drawn from the supply is equal to algebraic sum of currents flowing through individual resistances.
If I be the total current drawn from the supply, I1 be the current flowing through R1, I2 be the current flowing through R2 and I3 be the current flowing through R3 (as shown in fig. 5), then,
I = I1 + I2 + I3.
(iii) Voltage across each individual resistor is equal to supply voltage across parallel combination.
In fig. 5 all three resistances have the same terminal voltage ‘V’.
(iv) Current flowing through each resistance is given by the supply voltage divided by that resistance. In fig. 5,
