InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Obtain the expression for the equivalent resistance for 3 resistors connected in parallel and also write the expression of equivalent resistance for connection of' n' resistors. |
Answer» Solution :`rArr "" R_(1) ,R_(2) and R_(3)` are connected between a and b points as shown in figure.  `rArr` By connecting terminals of BATTERY of voltage V with a and b, I current will be passed through `R_(1) , R_(2), R_(3) " are " I_(1), I_(2) , I_(3)` respectively. `rArr` According to Ohm.s law, p.d. ACROSS `R_(1), R_(2), R_(3)` is V. `rArr V = I_(1) R_(I) rArr I_(1) = (V)/(R_(1)) "" `....(1) `V = I_(2) R_(2) rArr I_(2) = (V)/(R_(2)) "" ` ....(2) and V = `I_(3) R_(3) rArr I_(3) = (V)/(R_(3)) ` ... (3) `rArr` At point .a. , `I = I_(1) + I_(2) + I_(3) ""` ... (4) By substituting values of equation (1), (2) and (3) in equation (4), `I = (V)/(R_(1)) + (V)/(R_(2)) + (V)/(R_(3))` `therefore (I)/(V) = (1)/(R_(1)) + (1)/(R_(2)) + (1)/(R_(3)) "" `[ Dividing by V] `rArr " If"(I)/(V) = (1)/(R_(eq)) , ` then `(1)/(R_(eq) ) = (1)/(R_(1)) + (1)/(R_(2)) + (1)/(R_(3)) ` If `R_(eq) ` is represented as `R_(p)`, then `(1)/(R_(p)) = (1)/(R_(1)) + (1)/(R_(2)) + (1)/(R_(3))` `rArr` For EQUIVALENT resistance of .n. unequal resistors in parallel, `(1)/(R_(eq))= (1)/(R_(1)) + (1)/(R_(2)) + (1)/(R_(3)) + ...+ (1)/(R_(n))` `rArr` For equivalent resistance of .n. equal resistors of resistance R in parallel, `(1)/(R_(eq)) = (n)/(R)` `therefore R_(eq) = (R)/(n)` |
|