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Moving Charges And Magnetism

Question
CBSEENPH12039983

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 the 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 and l2 cm respectively. The magnitudes, of the resistor R and X, in ohm, are then, equal respectively, to

 

  • k (l2 -l1) and kl2

  • kl1 and k (l2-l1)

  • k (l2 - l1) and kl1

  • kl1 and kl2

Solution

B.

kl1 and k (l2-l1)

The balancing length for R (When 1, 2 are connected) be is l1 and balancing length for R + x (when 1, 3 is connected is l2)
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