Resistors in Series Formula
The resistor is important component used in electric circuits. Resistor have two ends. The resistance is given between its two ends. The number of resistors are connected in electric circuits. The ohm’s law is applicable to such combination of resistors.
There are two types of joining the resistors in circuits.
(1) Resistors in series
(2) Resistors in parallel
The three resistors are connected in a single line one after other. The resistors are said to be connected in ‘series’. Three resistors R1, R2 and R3 are connected in series as shown in above fig (1). The current flowing through the resistor is I and the potential difference between two points is V.
Let v1, be the voltage across R1, V2 across R2 and V3 across R3.
Then, V = v1 + v2 + v3 —– (1)
If the resistors are connected in series the same current flows through the each resistor. Rs is effective resistance, A/C to Ohm’s law,
V = IRs
V1 = I1R1, v2 = I2R2 and V3 = I3R3
Put there value of voltage in equation (1)
IRs = IR1 + IR2 + IR3
Rs = R1 + R2 + R3 —– (2)
The effective resistance of resistors is equal to the sum of their individual resistances. And it is larger that of the each individual resistances.
The resistors in series is used to increases the resistance in a circuit.
If n no. of resistors are connected in series then, equation (2) becomes,
Rs = R1 + R2 + R3 + —— + Rn —– (3)
The potential difference between two ends is equal to the sum of the potential differences across individual resistors.
Numericals on Resistors in Series Formula :
(1) Three resistors having resistance of 24 Ω, 22 Ω and 20 Ω are connected in series. If a potential difference of 26 V is applied across resistors, calculate the current flowing through the circuit and potential differences across each individual resistor.
Given:
R1 = 24 Ω, R2 = 22 Ω, R3 = 20 Ω
Rs is sum of individual resistances
So, Rs = R1 + R2 + R3
Rs = 24 + 22 + 20 = 66 Ω
The potential difference across 24 Ω, 22 Ω, 20 Ω be the v1, v2 and v3 respectively. I is the current flowing through the circuit.
A/C to Ohm’s law,
V = IR
V = V1 + V2 + V3
V = 26V
I = V/R = 26/66
∴ I = 0.39, I ≈ 0.4A
V1 = IR1 = 0.4×24 = 9.6 V
V2 = IR2 = 0.4×22 = 8.8 V
V3 = IR3 = 0.4×20 = 8 V
∴ The current flowing through circuit is 0.4 A
Potential difference across the resistances 24Ω, 22Ω and 20Ω are 9.6 V, 8.8 V, 8 V respectively.
(2) What is the effective resistance in circuit? If the two resistors having resistance 17Ω and 5Ω are connected in series
Given:
R1 = 17Ω, R2 = 5Ω
Effective resistance Rs = R1 + R2
= 17 + 5
Rs = 22Ω
∴ Effective resistance in circuits is 22Ω.