Question

A potentiometer wire has a length of 4 m and a resistance of 5 Ω. What resistance should be connected in series with a potentiometer wire and a cell of e.m.f. 2 V having internal resistance 1 Ω to get a potential gradient of 10^-3 V/cm ?

Answer 1

Given:

L = 4m

R = 5Ω

E = 2V

Internal resistance of cell,

r = 1Ω

K = 10^-3 V/cm

K = 10^-3 /10^-2

K = 0.1 V/m

To find:

R_E = ?

Formulae:

K = IR/L

I = E/(R + r + R_E)

Solution:

Since,

I = E/(R + r + R_E)

∴ K = IR/L

K = ER/(R + r + R_E)L

0.1 = (2 × 5)/(5 + 1 + R_E) × 4

0.1 × 4 × (6 + R_E) = 10

6 + R_E = 25

∴ R_E = 19Ω