A `10` meter long wire of uniform cross section of `20 Omega` resistance is used as a potentiometer wire. This wire is connected in series with a battery of `5V` along with an external resistance of `480 Omega` if an unknown emf `epsilon` is balanced at `600 cm` of this wire , calculate (i) the potential gradient of the potentiometer wire and (ii) the value of the unknown emf `epsilon`.

Answer

`2 xx 10^(-4) V//cm,0.12 V`

Explanation

Here `V = 5V, R = 480 Omega `resistance of potential meter wire `r = 20 Omega` Length of potentiometer wire `L = 1000 cm`
potential gradent
`K = ((V)/(R + r)) xx (r )/(L)`
`= (5)/((480 + 20)) xx (20)/(1000) = 2 xx 10^(-4) V//cm`
Unknown emf `epsilon` is balanced againest length `l = 600 cm ` so emf ` epsilon = Kl = 2 xx 10^(-2) xx 600 = 0.12V`