Derive an Expression for the Equivalent Resistance of Three Resistances Connected in Series

Series combination of resistances:

If a number of resistances are joined end to end so that the same current flows through each of them in succession, then the resistances are said to be connected in series.

Consider three resistances R, R₂and R connected in series. Suppose a current I flows through the circuit when a cell of voltage V is connected across the combination.

By Ohm’s law, the potential differences across the three resistances will be,

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Laws of resistances in series:

(i) Current through each resistance is same.

(ii) Total voltage across the combination = Sum of the voltage drops.

(iii) Voltage drop across any resistor is proportional to its resistance.

(iv) Equivalent resistance = Sum of the individual resistances.

(v) Equivalent resistance is larger than the largest individual resistance.

Electricity:

Change the position of ammeter to anywhere in between the resistors. Note the ammeter reading each time.

Do you find any change in the value of current through the ammeter?

Observations and Conclusions:

It is observed that the value of the current in the ammeter is the same, independent of its position in the electric circuit.

It means that in a series combination of resistors the current is the same in every part of the circuit or the same current flows through each resistor.