Question

An insulating pipe of cross-section area '$A$' contains an electrolyte which has two types of ions, their charges being $-e$ and $+2e$. A potential difference applied between the ends of the pipe result in the drifting of the two types of ions, having drift speed $=v(-veion)$ and $v/4(+veion)$. Both ions have the same number per unit volume $=n$. The current flowing through the pipe is

• A. $nevA/2$
• B. $nevA/4$
• C. $5nevA/2$
• D. $4nevA/2$

Answer 1

The correct option is A $nevA/2$

As the pipe is filled with an electrolyte so net cutent $I$ is given as

$I$=$I_2-I_1$

$I_2$=positive ion moving along the field.

$I_1$=negative ion moving opposite to the field.

now $I$=-$I_2$-(-$I_1$)

hence $I$=-$I_2$+$I_1$

$I=[-2neA(\frac{v}{4}\left)\right]+\left[neAv\right]$

$I=nev\left(\frac{A}{2}\right)$

NOTE: If the solution is placed in an electric field,the positive ion will move inside the solution(i.e along the field) and the negative ion will move opposite to the field.