Question

An I0m long uniform metallic wire having a resistance of 20Ω IS used as a  potentiometer wire. This wire is connected in series with another resistance of 480Ω
and a battery of emf 5V having negligible internal resistance. If an unknown emf e is balanced across 6m of the potentiometer wire, calculate

1) the potential gradient across the potentiometer wire

2) the value of the unknown emf e.

Answer 1

`l_1 = 10 m`

R = 20 Ω

`R_1 = 480 Ω`

V = 5 V

balancing lenght = `l_2  = 6m`

1) Potential gradient = `k = V/L = 5/6 = 0.83 "V/m"`

2) `E_1/E_2 - l_1/l_2`

`5/E_2 = 10/6`

`5 xx 6 = E_2 xx 10`

`(5 xx 6)/10 = E_2`

`:. E_2 = 3V`