Obtain an expression for equivalent resistance of two resistors connected in a series combination.

Explanation

Let `C_(1), C_(2)` - capacitance of 2 capacitors connected in series
Q- charge on each capacitor
`V_(1) V_(2)`-pd across `C_(1)` and `C_(2)`
V-total voltage drop across the combination
Then `V = V_(1) + V_(2)`.....(1)
Also `Q = C V`
`V_(1) = (Q)/(C_(1))` and `V_(2) = (Q)/(C_(2))`
If system of capacitors is replaced by a single capacitor of equivalent capacitance `C_(S)` then `V_(S) = (Q)/(C_(S))`
(1) `rArr (Q)/(C_(S)) = (Q)/(C_(1)) + (Q)/(C_(2))`
`(1)/(C_(S)) = (1)/(C_(1)) + (1)/(C_(2))`