JEE Main · 2005 · 08 May 2005 · Offline · Chapter_pending

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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) $\frac{q}{1 + \frac{z _{2}}{z _{1}}}$ ✓ Correct
(C) $q \frac{z _{1}}{z _{2}}$
(D) $q \frac{z _{2}}{z _{1}}$

Answer: (B)

Solution

By Faraday's law the deposited mass is

m = z q

, so equal masses require

z_{1} q_{1} = z_{2} q_{2}

, with

q_{1}

and

q_{2}

the charges through the copper and silver cells. Using the total

q = q_{1} + q_{2}

together with

q_{1} = q_{2} \frac{z _{2}}{z _{1}}

, we get

q = q_{2} (\frac{z _{2}}{z _{1}} + 1)

, so the silver cell carries

q_{2} = \frac{q}{1 + \frac{z _{2}}{z _{1}}}

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

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