Question

Two voltameters, one of copper and another of silver, are joined in parallel. When a total charge $q$ flows through the voltameters, equal amount of metals are deposited. If the electrochemical equivalents of copper and silver are $z_1$ and $z_2$ respectively, the charge which flows through the silver voltameter is

• A. $\frac{q}{1+\frac{z_1}{z_2}}$
• B. $\frac{q}{1+\frac{z_2}{z_1}}$
• C. $q\frac{z_1}{z_2}$
• D. $q\frac{z_2}{z_1}$

Answer 1

Answer: (A)

$\frac{q}{1+\frac{z_1}{z_2}}$

Here, equal amount of metals are deposited hence

$z\propto \frac{1}{q}$

$\Rightarrow z_1\propto \frac{1}{q_1}$ and $z_2\propto \frac{1}{q_2}$

$\therefore \frac{z_2}{z_1}=\frac{q_1}{q_2}$ ....................(1)

Now, total charge flowing through the voltmeters is

$q=q_1+q_2$

$\therefore \frac{q}{q_2}=\frac{q_1}{q_2}+1$

$\therefore q_2=\frac{q}{1+\frac{q_1}{q_2}}$

from (1)

$q_2=\frac{q}{1+\frac{z_1}{z_2}}$