A potentiometer wire of length L and a resistance r are connected in series with a battery of e.m.f. E0 and a resistance r1. An unknown e.m.f. E is balanced at a length l of the potentiometer wire. The e.m.f. E will be given by
- E0lL
- LE0r(r + r1)l
- LE0rlr1
- E0r(r + r1) lL
Answer
(4) E0r(r + r1) lL
Solution
Current in the main circuit: I = E0r + r1
Potential drop across the whole wire = Ir = E0rr + r1
Potential gradient: k = E0r(r + r1)L
E = kl = E0r(r + r1) lL
Answer: (4)