System of Resistors - Resistors in Series

When resistors are connected in such a way that their ends are joined one after the other in a single line, they are said to be connected in series. This arrangement is commonly used to increase the total resistance of a circuit.

Resistors in series

The same current (I) flows through all resistors in a series connection because there is only one current path. The value of current is I, and the potential difference between $C$ and $D$ is $V$.

The three resistors, R₁, R₂​, and R₃, are connected in series in the circuit. If V₁, V₂, and V₃ represent the potential differences of each resistor, R₁, R₂, and R₃, respectively, then​​​​​

V=V₁+V₂+V₃−−−−−−−−(1)

If R_s ($S$ for series) is the effective resistance between $C$ and $D$, then, according to Ohm’s law:

V=IR_s

 V1=IR₁, V2=IR₂, V3=IR₃​

Substituting all these in equation (1), we get:

IR_s = IR₁ + IR₂ + IR₃

R_s​ = R₁​ + R₂​ + R₃​

If $n$ resistors are connected in series, then:

R_s = R₁ + R₂ + R₃ +⋯+ R_n

1. In a series connection of resistors, the same current flows through each resistor, as there is only one path for the current to travel.
2. The effective resistance of the resistors is equal to the sum of their individual resistances, calculated as R_s = R₁ + R₂ + R₃ +⋯+ R_n.
3. The potential difference across the entire series arrangement is equal to the sum of the potential differences across each individual resistor.
4. The effective resistance in a series connection is always greater than the resistance of any individual resistor.
5. The primary purpose of this configuration is to increase the overall resistance in a circuit.