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 be connected in series.

In the figure above, three resistors R₁, R₂ and R₃ are connected in series across the points A and B.

Hence, the current (I) flowing through each of the resistors is same but the total voltage of the battery is divided.If the voltage drops across V₁, V₂ and V₃ are R₁, R₂ and R₃ respectively then,
V = V₁ + V₂ + V₃ …………….(i)
Now, if the resistor R instead of these three resistances R₁, R₂ and R₃ is connected in such a way that the current flowing through the circuit remains the same, then R is called equivalent resistance of the circuit.For an equivalent resistor,

V = IR …………….(ii)

According to Ohm’s law,
R₁ voltage drops across, V₁ = IR₁ …………..(iii)
R₂ voltage drops across, V₂ = IR₂ …………..(iv)
R₃ voltage drops across, V₃ = IR₃ …………..(v)
Adding (iii), (iv) and (v):
V₁ + V₂ + V₃ = IR₁ + IR₂ + IR₃ ……(vi)

Or, V = IR = I(R₁ + R₂ + R₃) Or, 
R = R₁ + R₂ + R₃

Thus, in series connection the equivalent resistor R is equal to the sum of all the resistors connected in series.