An insulating pipe of cross-sectional area A contains an electrolyte which has monovalent negative ions and bivalent positive ions having drift speeds v and v/4 respectively on applying potential difference across the pipe. Both the ions have same number density equal to 'n'. The current flowing through the pipe is

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Solution

As the number of ions flowing through the pipe is "n". The current(i) flowing through a pipe is directly proportional to the number of ions(n) , a number of electrons(e) flowing through the same, the drift velocity(Vd) of the electrons and the area of cross-section of the pipe(A).

Thus, $i = n e A V_{d},$

Here, $i_{1} = n e A V$
and $i_{2} = \frac{n 2 e A V}{4} .$

Hence the net current through the pipe is $i_{n e t} = i_{1} + i_{2},$

$i_{n e t} = n e A V + \frac{n e A V}{2} .$

$i_{n e t} = \frac{3}{2} n e A V$

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