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What is parallel connection of resistors ? Derive equation of equivalent resistance in parallel connection. |
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Answer» Solution :`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. |
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