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On interchanging the resistance thebalance point of a meter bridge shifts to the left by 10 cm. The resistance of their seris combination is 1 k Omega. How much was the resistance on the left slot before the interchange ? |
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Answer» 990 `Omega` In first situation `(R_(1))/(R_(2))= (l)/(100 - l) "" `... (1) `l_(2) = 100- l` By moving the place `(R_(2))/(R_(1)) = (l - 10)/(110 - l) "" `.... (2) `l_(2) = 100 - (l - 10)` `= 100 - l+ 10` `= 110 - l ` Now ` (R_(1))/(R_(2)) xx (R_(2))/(R_(1)) = 1 ` `(l)/(100 - l) xx (l - 10)/(110 - l) =1 ` `therefore l^(2) - 10 l = 11000 - 100 l - 110 l + l^(2)` `therefore= 200 l = 11000` `therefore l = 55 ` cm Now from EQ. (1) `(R_(1))/(100 - R_(1))= (55)/(100 - 55)` `[ because R_(1) + R_(2) = 1000 , therefore R_(2) = 1000 - R_(2) ] ` `therefore (R_(1))/(1000 - R_(1))= (55)/(45)` = `(11)/(9)` , ` therefore9 R_(1) = 11000 - 11 R_(1)` `therefore 20 R_(1) = 11000` `therefore R_(1) = 550 Omega` |
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