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The reading of an ideal ammeter, in the circuit shown here, equals (i) I when key K_1is closed but key K_2 is open , (ii) I/2when both keys K_1 and K_2are closed. Find the expression for the resistance of X in terms of the resistance R and S. |
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Answer» Solution : We know that resistance of an ideal AMMETER is zero. (i)When only key `K_1`is closed, the current flowing through the ammeter is given as : `I. = (epsi)/( R + (SX)/(S + X))` and the current flowing through the ammeter is given as : `I/2 = (S)/(S + X).I.= ( (S)/(S+X)) .(epsi)/(R +(SX)/(S + X)) = (S epsi)/((S + X)R+SX)`...(ii) Multiplying (ii) by 2 and then equating with (i), we GET `(epsi)/(R+X) = (2S epsi)/((S + X)R+ SX)` ` RARR (S+X) R + SX = 2S (R+X)" or" SR + XR + SX = 2SR + 2SX` ` rArr XR - SX = SR`or`X = (RS)/((R - S))` |
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