Question

A potentiometer wire has a length 5 m and a resistance 10 Ω. The driving cell has an e.m.f. of 5 V and an internal resistance of 5 Ω. The distances at which null points are obtained when two cells of e.m.f. 1.5 V and 1.3 V are connected so as to (1) assist and (2) oppose each other are respectively:

विकल्प

• 2.1 m, 0.15 m

• 2.8 m, 0.20 m

• 3.5 m, 0.25 m

• 4.2 m, 0.30 m

Answer 1

4.2 m, 0.30 m

Explanation:

Given: Length (L) = 5 m

Resistance (R) = 10 Ω

Driving emf (E) = 5 V

Internal resistance (r) = 5 Ω

Current in circuit (I) = `E/(R + r)`

= `5/(10 + 5)`

= `5/15`

= `1/3` A

Potential gradient (k) = `(I R)/L`

= `(1/3 xx 10)/5`

= `10/15`

= `2/3` V/m

Cell assisting (E) = 1.5 + 1.3

= 2.8

Null point length (l) = `E/k`

= `2.8/(2/3)`

= (2.8 xx 3)/2`

= `8.4/2`

= 4.2 m

Cell opposing (E) = 1.5 − 1.3

= 0.2 V

Null point length (l) = `E/k`

= `0.2/(2/3)`

= `(0.2 xx 3)/2`

= `0.6/2`

= 0.30 m