Explain the series connections of resistors and derive the formula of equivalent resistance.

The resistors are connected across two points in the circuit in such a way that the current flowing through each resistor is the same and only one path is available for it to flow, then the resistors are said to be connected in series.

From the figure, if voltage drops across R₁, R₂ & R₃ are V₁, V₂ & V₃ respectively.

Moreover, same current I is flowing to all the three resistors.

Using Ohm’s Law

R₁ voltage drops across V₁ = IR₁

R₂ voltage drops across V₂ = IR₂

R₃ voltage drops across V₃ = IR₃

From above three equations

IR = IR₁ + IR₂ + IR₃

R = R₁ + R₂ + R₃