Obtain an expression for equivalent resistance of two resistors connected in parallel.

Explanation

Equivalent resistance is the concentrated or lumped resistance hat would cause the same power loss as the actual small resistacne value distributed throughout a circuit.
Connect two resistors `.R_(1). and .R_(2).` in parallel to one another between the points A and B. Connect this combination to a battery of potential .V..

Here the potential difference across `R _(1) and R_(2)` will be equal to battery voltage. But the total current I following in the circuit branches as `I _(1)` through `R_(1)` and `I _(2)` through `R_(2).`
Since there cannot be accumulation of charges at any point
`I = I_(1) + I _(2) " "...(i)`
Using Ohm.s law.
`I = V/R, I _(1) = (V)/(R _(1)), I _(2) = (V)/(R_(2)) " "...(ii)`
Substituting the above set of equations (ii) in equation (i) we get
`V/R = (V)/(R_(1)) + (V)/(R _(2)) = V [ (1)/(R_(1)) + (1)/(R _(2)) ] `...(iii)
Divide equation (iii) throughout by V we get
`implies (1)/(R) = (1)/(R_(1)) + (1)/(R_(2))`