InterviewSolution
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InterviewSolution
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A resistance of `R Omega` draws current from a potentiometer. The potentiometer has a total resistance `R_(0) Omega`. A voltage V is supplied to the potentiometer. Derive an expression for the voltage fed into the circuit when the slide contact is in the middle of potentiometer. |
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Answer» When slide is in the middle of the potentiometer wire, only half of the resistance of potentiometer wire `( = R_(0)//2)` will be between the points A and B. Hence effective resistance `(R_(1))` between A and B is `1/R_(1) = 1/R + 1/(R_(0)//2) or R_(1) = (R_(0)R)/(R_(0) + 2R)` Total resistance between A and C `= R_(1) + R_(0)/2` Current through the potentiometer wire will be `I=V/(R_(1) + R_(0)//2) = 2V/(2 R_(1) +R_(0))` The voltage `V_(1)` taken from the potentiometer will be the product of current I and resistance `R_(1)` , i.e., `V_(1) = IR_(1) = ((2V)/(2R_(1) + R_(0))) xx R_(1)` `=(2V)/((2(R_(0)R)/(R_(0)+2R))+R_(0)) xx (R_(0)R)/(R_(0)+2R)` ` = ( 2 VR)/( 2R + R_(0) + 2R) = (2VR)/(R_(0) +4R)` |
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