In Fig. `6.16`, `AB` is a `1 m` long uniform wire of `10 Omega` resistance. Other data are shows in the figure. Calculate (i) potential gradient along `AB` and (ii) length of AO when galvanometer shows no deflection.

Explanation

(i) Current in wire `Ab` is `l = 2//(15 + 10) = 2//25 A`
potential difference across `AB` is
`V = lR = 2//25 xx 10 = 0.8 V`
Potential gradient along `AB` is
`k = V//l = 0.8//1 = 0.8 V`
(ii) Current through `0.3 Omega` is
`(1.5)/(1.2 + 0.3) = 1 A`
Potential difference acros `0.3 Omega`is `1 xx 0.3 = 0.3 V`
Let `l_(1)` be the length`AO`, then
`0.3 = 0.8 xx l_(1)`
or `l_(1) = 0.3//0.8 = 0.375 m`