question_answer

A silver voltameter of resistance 2 ohm and a 3 ohm resistor are connected in series across a cell. If a resistance of 2 ohm is connected in parallel with the voltameter, then the rate of deposition of silver                                                     [EAMCET 1983]

A)            Decreases by 25%              

B)            Increases by 25%

C)            Increases by 37.5%            

D)            Decreases by 37.5%

Correct Answer: D

Solution :

                   Initially current through the voltameter \[{{i}_{1}}=\frac{V}{(3+2)}=\frac{V}{5}\]                    Finally main current \[i=\frac{V}{3+1}=\frac{V}{4}\]                    Hence current through voltameter \[{{i}_{2}}=\frac{V}{8}\]                    \[\because \]  Rate of deposition \[(R)=\frac{m}{t}=Zi\]Þ \[R\propto i\]                    \ % drop in rate \[=\frac{{{R}_{2}}-{{R}_{1}}}{{{R}_{1}}}\times 100=\frac{{{i}_{2}}-{{i}_{1}}}{{{i}_{1}}}\times 100\]            \[=\frac{\left( \frac{V}{8}-\frac{V}{5} \right)}{\frac{V}{5}}\times 100=-37.5%\]