Question

Derive an expression for equivalent resistance when two resistors R1 and R2 are connected in series.

Answer 1

If they are in series, then current passed through one resistance will also pass through another.
So I1=I2=I......... (a)
Now looking for potential difference across the combination
V=V1+V2
as V=IR
So IR=I1R1+I2R2
Using (a)
→R=R1+R2

This is the expression you are searching for,

Answer 2

Equivalent resistance in series:

• Let's assume that two resistors R1 and R2 are connected in series.

• Let the net potential difference applied by the battery be V and the net current be I.

We know that : In series combination, the net potential difference in the circuit will be equal to the addition of individual potential difference across each resistance.

$V = V1 + V2$

$\implies IR_{eq} =I(R1) + I(R2)$

$\implies IR_{eq} =I(R1+ R2)$

$\implies R_{eq} =R1+ R2$

[Hence derived]