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| 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» <html><body><p></p>Solution :`rArr "" R_(1) ,R_(2) and R_(3)` are connected between a and b points as shown in figure. <br/><img src="https://doubtnut-static.s.llnwi.net/static/physics_images/KPK_AIO_PHY_XII_P1_C03_E01_035_S01.png" width="80%"/><br/> `rArr` By connecting terminals of <a href="https://interviewquestions.tuteehub.com/tag/battery-893842" style="font-weight:bold;" target="_blank" title="Click to know more about BATTERY">BATTERY</a> 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. <br/> `rArr` According to Ohm.s law, p.d. <a href="https://interviewquestions.tuteehub.com/tag/across-367070" style="font-weight:bold;" target="_blank" title="Click to know more about ACROSS">ACROSS</a> `R_(1), R_(2), R_(3)` is V. <br/> `rArr V = I_(1) R_(I) rArr I_(1) = (V)/(R_(1)) "" `....(1) <br/> `V = I_(2) R_(2) rArr I_(2) = (V)/(R_(2)) "" ` ....(2) <br/>and V = `I_(3) R_(3) rArr I_(3) = (V)/(R_(3)) ` ... (3) <br/> `rArr` At point .a. , <br/> `I = I_(1) + I_(2) + I_(3) ""` ... (4) <br/> By substituting values of equation (1), (2) and (3) in equation (4), <br/> `I = (V)/(R_(1)) + (V)/(R_(2)) + (V)/(R_(3))` <br/> `therefore (I)/(V) = (1)/(R_(1)) + (1)/(R_(2)) + (1)/(R_(3)) "" `[ Dividing by V] <br/> `rArr " If"(I)/(V) = (1)/(R_(eq)) , ` then <br/> `(1)/(R_(eq) ) = (1)/(R_(1)) + (1)/(R_(2)) + (1)/(R_(3)) ` <br/> If `R_(eq) ` is represented as `R_(p)`, then `(1)/(R_(p)) = (1)/(R_(1)) + (1)/(R_(2)) + (1)/(R_(3))`<br/> `rArr` For <a href="https://interviewquestions.tuteehub.com/tag/equivalent-446407" style="font-weight:bold;" target="_blank" title="Click to know more about EQUIVALENT">EQUIVALENT</a> resistance of .n. unequal resistors in parallel,<br/> `(1)/(R_(eq))= (1)/(R_(1)) + (1)/(R_(2)) + (1)/(R_(3)) + ...+ (1)/(R_(n))`<br/> `rArr` For equivalent resistance of .n. equal resistors of resistance <a href="https://interviewquestions.tuteehub.com/tag/r-611811" style="font-weight:bold;" target="_blank" title="Click to know more about R">R</a> in parallel,<br/> `(1)/(R_(eq)) = (n)/(R)` <br/> `therefore R_(eq) = (R)/(n)`</body></html> | |