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Question
Find the expression for resistors connected in series.
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Solution
When two or more resistors are joined from end to end, the resistances are connected in series.
The current in series remains the same across all the resistors.
The potential difference is the sum of potential differences across all the individual resistors.
V = V1 + V2 + V3 … (1)
Let I be the current in the circuit.
On applying Ohm’s law to the entire circuit, we get
V = IRs … (2)
Here, Rs is the combined resistance of the circuit.
Now, applying Ohm’s law to individual resistances, we get
V1 = IR1
V2 = IR2
V3 = IR3 ......(3)
From equations (1), (2) and (3), we get
IRs = IR1 + IR2 + IR3
∴ Rs = R1 + R2 + R3
Here, Rs is the resultant resistance. Thus, the resultant resistance of a series combination of resistors is the sum of individual resistances.
The resultant resistance is greater than all the resistances.
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