Combination of resistors: Resistors in series and parallel

Combination of resistors

In simple circuits with resistors, Ohm’s law can be applied to find the effective resistance. The resistors can be connected in series and parallel.

1. Resistors in series

Let us consider the resistors of resistances R1, R2, R3 and R4 connected in series as shown in Fig 2.6.

When resistors are connected in series, the current flowing through each resistor is the same. If the potential difference applied between the ends of the combination of resistors is V, then the potential difference across each resistor R1, R2, R3 and R4 is V1, V2, V3and V4 respectively.

The net potential difference V = V1 + V2 + V3 + V4

By Ohm’s law

V1 = IR1, V2 = IR2, V3 = IR3, V4 = IR4 and V = IRs

where RS is the equivalent or effective resistance of the series combination.

Hence, IRS = IR1 + IR2 + IR3 + IR4 or RS = R1 + R2 + R3 + R4 Thus, the equivalent resistance of a number of resistors in series connection is equal to the sum of the resistance of individual resistors.

2. Resistors in parallel

Consider four resistors of resistances R1 , R2 , R3 and R4 are connected in parallel as shown in Fig 2.7. A source of emf V is connected to the parallel combination. When resistors are in parallel, the potential difference (V) across each resistor is the same.

A current I entering the combination gets divided into I1, I2, I3 and I4 through R1, R2, R3 and R4 respectively,

such that I = I1 + I2 + I3 + I4.

Thus, when a number of resistors are connected in parallel, the sum of the reciprocal of the resistance of the individual resistors is equal to the reciprocal of the effective resistance of the combination.