Question

A $3\Omega$ resistor and a silver voltameter of resistance $2\Omega$ are connected in series across a cell. How will the rate of deposition of silver be affected if a resistance of $2\Omega$ is connected in parallel with the voltameter?

• A. it will decrease by 25%
• B. it will increase by 25%
• C. it will increase by 37.5%
• D. it will decrease by 37.5%

Answer 1

The correct option is D it will decrease by 37.5%

Given

Resistance in series with silver voltameter is $R_1=3\Omega$

Resistance of silver voltmeter is $R_{si}=2\Omega$

Resistance in parallel with silver voltameter is $R_2=2\Omega$

The rate of deposition of silver is

$\frac{dm}{dt}=ZI=Z\frac{V}{R}$

Initially, $R_{‘}1$ is in series with silver voltmeter, hence total resistance of the branch is

$R_s=R_1+R_{si}=3+2=5\Omega$

When a resistance $R_2$ is connected in parallel with the voltmeter, the

resistance across voltmeter is

$R_p=\frac{R_{si}{R}_2}{R_{si}+R_2}$

$R_p=\frac{\left(2\right)\left(2\right)}{2+2}=\frac{4}{4}=1$

Hence, the total resistance of the branch is now

$R_s^{\prime }=R_1+R_p=3+1=4$

Current in the first case = $Z\frac{V}{5}$

Current in the second case =$Z\frac{V}{8}$ as the current divides

equally in the 2 branches.

The percentage change in rate of deposition is

$\frac{\frac{1}{8}-\frac{1}{5}}{\frac{1}{5}}\times 100=\frac{-3}{8}\times 100=-37.5$%

Hence, the rate of deposition will decrease by 37.5%.