Electricity: Combination of Resistors

Total resistance of resistors in series combination
Total resistance of resistors in parallel combination

These notes are based on the chapter Electricity class 10 science of NCERT book and CBSE syllabus.

Resistors are joined in two ways, i.e. in series and in parallel.

Resistors in Series

When resistors are joined from end to end, it is called the series combination.

You can compare such a combination as people standing in a line and one person is holding the hand of the next person and so on.

In this case, the total resistance of the system is equal to the sum of the resistance of all the resistors in the system. Bulbs in decorative light for festivals are joined in this fashion.

Following figure shows a circuit in which three resistors R₁, R₂ and R₃ are joined in series.

Fig: Resistance in Series

Let total resistance = R

Resistance of resistors are R₁, R₂, R₃, … R_n

Therefore, R = R₁ + R₂ + R₃ + …………+ R_n

Resistors in Parallel

When all the resistors are joined in a way that positive ends of all of them are joined together and so do the negative ends, it is called a parallel combination.

Electrical appliances in household wiring are joined in htis fashion. When resistors are joined in parallel, the reciprocal of total resistance of the system is equal to the sum of reciprocal of the resistance of resistors. Following figure shows a circuit in which three resistors R₁, R₂ and R₃ are joined in parallel.

Fig: Resistance in Parallel

Let total resistance = R

Resistance of resistors are R₁, R₂, R₃, … R_n

`1/R=(1)/(R_1)+(1)/(R_2)+(1)/(R_3)+…….+(1)/(R_n)`