The driver cell of a potentiometer has an emf of 2 V and negligible internal. resistance. The potentiometer wire has at resistance of 3Ω. Calculate the resistance needed in series with the wire if P.d of 5 mV is required across the whole wire. The wire is 100cm long and a balance length of 60 cm obtained for a thermocouple of emf E. What is the value of E.

Solution:

Let AB be the potentiometer wire and R be the resistance to be placed in series so that the P.d across AB is mV and R_AB = 3Ω

I = $\frac{2}{{R + 3}}$

P.d across AB (V_AB)= I R_AB

Or, 5 x 10^-3 = $\frac{2}{{R + 3}}$ x 3  

Or, 5R = 5985

∴ R = 1197 Ω

P.d across 100cm of wire = 5mV

∴ P.d. across 60 cm of wire = $\frac{{50 \times 60}}{{100}}$ = 3mV

∴ The required resistance is 1197 Ω and the value of thermocouple of e.m.f. is 3mV.