Derive an expression for the equivalent resistance of three resistors `R_(1) R_(2)` and `R_(3)` connected in series.

Explanation

Total potential difference across a combination of resistors in series is equal to the sum of potential difference across the individual resistors.
`V=V_(1)+V_(2)+V_(3)`
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 ir, 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
`V_(1)=IR_(1)`
`V_(2) =IR_(2)`
`V_(3)=IR_(3)`

But `" " V =V_(1)+V_(2)+V_(3)`
`IR =IR_(1)+IR_(2)+IR_(3)` ,
`R=R_(1)+R_(2)+R_(3)`