A potentiometer circuit is set up as shown. The potential gradient, across the potentiometer wire, is 
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 
cm and 
cm respectively The magnitudes, of the resistors R and X, in ohms, are then, equal, respectively, to
and 
and 
and 
and 
Text Solution
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When the two way key is switched off, then
The current flowing in the resistors R and X is 
(i)
When the key between the terminals 1 and 2 is plugged in, then
potential difference across 
(ii)
where 
is the potential gradient across the potentiometer wire.
When the key between the terminals 1 and 3 is plugged in, then potential difference across 
(iii)
From equation (ii), we get
(iv)
From equation (iii), we get
(Using (i)) 
(Using (iv))
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