Circuit for the measurement of resistance by potentiometer is shown in figure. The galvanometer is first connected at point A and zero deflection is observed at length `PJ = 10 cm.` In second case, it is connected at point C and zero deflection is observed at a length 30 cm from P, then the unknown resistance X is .

Options

A. 2 R
B. `R//2`
C. `R//3`
D. 3 R

Answer

A

Explanation

a. In potentiometer wire, potential difference is directly proportional to length. Let the potential drop of unit length of
a potentiometer wire be K.

For zero deflection, the current will flow independently in two
circles :
`IR = K xx 10` .......(i)
` I R + I X = K xx 30` .......(ii)
Subtracting Eq. (ii) from Eq. (i), we get
`IX = k xx 20 ` ......(iii)
Dividing Eq. 9i) by Eq. (ii), we have
`R/X = 1/2` .