Answer to Question #81096 in Electric Circuits for Rabin

Question

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

Answer 1

Write Ohm’s law for the circuit:
V=R_wire I+R_needed I,
where
R_wire I=0.005 ⇨ I=0.005/R_wire .
Thus,
R_needed=(V-R_wire I)/I=R_wire (V/0.005-1)=3(2/0.005-1)=1197 Ω.

R_wire=ρL/S ⇨ρ/S=3,
since L=100 cm = 1 m.
E=I 0.6ρ/S=V/(R_wire+R_needed )·0.6 ρ/S=2/(3+1197)·0.6·3=0.003 V.