What is parallel connection of resistors ? Derive equation of equivalent resistance in parallel connection.

Explanation

`rArr` If ends of two or more resistors are joined together, then such arrangement is called parallel connection of resistors.
`rArr` In parallel, voltage remains same in all resistors and currents flowing through resistors are different The sum of currents in all resistors is equal to the current flowing in circuit through battery.
`rArr` Suppose `R_(1) and R_(2)` two resistors are connected as shown in figure at a and b points with connection of battery of terminal voltage V, I current is passing in circuit and it will be divided in two parts at point a.

Let , currents passing through `R_(1) and R_(2) ` are `I_(1) and I_(2)` respectively.
`rArr " At .a. point" , I = I_(1) + I_(2) " " `....(1)
`rArr` According to Ohm.s law,
p.d. about `R_(1)`,
`V = I_(1) R_(1) rArr I_(1) = (V)/(R_(1)) " " `....(3)
By substituting values in equation (1) from equation (2) and equation (3),
`I = (V)/(R_(1)) + (V)/(R_(2))`
`therefore (I)/(V) = (I)/(R_(1)) + (I)/(R_(2)) " " [ because " Dividing by " V] `
but `(1)/(V) = R_(eq)`
`therefore (I)/(R_(eq)) = (I)/(R_(I)) + (I)/(R_(2))`
`rArr` thus, in parallel connection inverse of equivalent resistance is equal to the sum of inverse of all resistances.
`rArr ` Hence, equivalent resistance is smaller than the smallest resistance.