Question

derive an expression for the equivalent resistance of three resistors R1 R2 and R3 connected in series

Answer 1

Total potential difference across a combination of resistors in series is equal to the sum of potential difference across the individual resistors.

V = V1 + V2 + V3

Let I be the current in the circuit. The current through each resistor is also I. It is possible to replace the three resistors joined in series by an equivalent resistor of resistance R. Applying Ohm's law,

V = IR

On applying Ohm's law to the three resistors respectively we further have

V1 = IR1

V2 = IR2

V3 = IR3

(I have attached the figure)

But V = V1+ V2 + V3

IR = IR1 + IR2 + IR3

Answer 2

$\textbf{Answer is in Attachment !}$