Question

Figure below shows a uniform manganin wire XY of length 100 cm and resistance 9Ω connected to an accumulator D of emf 4 V and internal resistance 1Ω through a variable resistance R. E is a cell of emf 1.8 V connected to the wire XY via a jockey J and a central zero galvanometer G. It is found that the galvanometer shows no deflection when XJ = 80 cm. Find the value of R.

Answer 1

We have,

E = Kl

1.8 = K x 0.80

K = 2.25 V/m = 0.0225 V/cm

Potential gradient along the wire XY,

K = V/l

0.0225 = V/100

∴ V = 2.25 volt.

Current in the potentiometer wire Xy is,

\(I=\frac{4}{1+R+9}\)

Now,

V = I x Resistance of wire

\(2.25=\frac{4}{10+R}\times9\)

\(10+R=\frac{9\times 4}{2.25}\)

R = 6Ω