A potentiometer circuit is set up as shown. The potential gradient, across the
potentiometer wire, is k volt/cm and the ammeter, present in the circuit, reads
1.0 A when two way key is switched off. The balance points, when the key
between the terminals (i) 1 and 2 (ii) 1 and 3, is plugged in, are found to be at
lengths l1 cm and l2 cm respectively. The magnitudes, of the resistors R and X, in ohms,
are then, equal, respectively, to:

iR space equals space kl subscript 1
and space iR space equals space kl subscript 1
Given space straight i space equals space 1 space straight A
straight R space equals space kl subscript 1 space.... space left parenthesis straight i right parenthesis
straight R space plus space straight X space equals space kl subscript 2 space..... space left parenthesis ii right parenthesis
Subtracting space eq comma space left parenthesis straight i right parenthesis space from space eg. space left parenthesis ii right parenthesis space comma space we space get
space straight X space equals space straight k space left parenthesis straight l subscript 2 minus space straight l subscript 1 right parenthesis space
therefore,
R=kL1
​X=k(L2-L1)
 
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