Series Circuit Formula

In a series circuit, all the current moves through each individual component because there is only one unidirectional path for the current movement. In a series circuit, the total resistance (R_s) is the sum of the individual resistance of the resistors (R₁, R₂, R₃,…R_n):

R_s = R₁ + R₂ + R₃ + … + R_n

The total voltage drop (V_s) in a series circuit is equal to the sum of the individual voltage drops (V₁, V₂, V₃,…V_n):

V_s = V₁ + V₂ + V₃ + … + V_n

Derivation of Series Circuit formula

In a series circuit, the current is the same at every point because there is only one path for the current to flow. We can use this fact to derive the formula for the total resistance in a series circuit.

Let’s assume we have a series circuit with n resistors, each with R₁, R₂, R₃, …, R_n resistance. The total resistance of the circuit, which we will denote as R_T, is the sum of the individual resistances:

R_T = R₁ + R₂ + R₃ + … + R_n

We can derive this formula by considering the voltage drop across each resistor. The formula gives the voltage drop across a resistor:

V = IR

Where V is the voltage drop, I is the current, and R is the resistance. Since the current is the same at every point in the circuit, we can use the same current I in each voltage drop formula. Therefore, the voltage drop across each resistor is:

V₁ = I * R₁

V₂ = I * R₂

V₃ = I * R₃

…

V_n = I * R_n

The total voltage drop across the entire circuit is the sum of the voltage drops across each resistor:

V_T = V₁ + V₂ + V₃ + … + V_n

Substituting the voltage drop formulas for each resistor, we get:

V_T = I × R₁ + I × R₂ + I × R₃ + … + I × R_n

We can factor out the current I from each term to get:

V_T = I × (R₁ + R₂ + R₃ + … + R_n)

The total resistance R_T is defined as the ratio of the total voltage drop V_T to the current I:

R_T = V_T / I

Substituting the expression for V_T, we get:

R_T = I × (R₁ + R₂ + R₃ + … + R_n) / I

The current I cancels out, leaving us with the formula for the total resistance in a series circuit:

R_T = R₁ + R₂ + R₃ + … + R_n

This equation shows that the total resistance of a series circuit is straightforward addition of the individual resistances. This is an important property of series circuits because it allows us to obtain the total resistance of a circuit by adding the individual resistances of its elements.

A series circuit is one of the most important concepts of electrical and electronics courses. In a series circuit, all the components are sequentially arranged and connected with each other to form a single current path. The installed total resistance is the sum of all individual resistors’ resistances. Hence, the total voltage drop is also the sum of the individual voltage drops across the respective resistors. This article will cover the equations, simplifications, and uses of series circuit systems.