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Current Electricity question

2005 · Shift 0 · Q166
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Current Electricity question

2005 · Shift 0 · Q166

JEE MainPhysicsCurrent ElectricityMCQ+4 / −1
Two voltmeters, one of copper and another of silver, are joined in parallel. When a total charge qqq flows through the voltmeters, equal amount of metals are deposited. If the electrochemical equivalents of copper and silver are Z1{Z_1}Z1​ and Z2{Z_2}Z2​ respectively the charge which flows through the silver voltmeter is
  1. A
    q1+Z2Z1{q \over {1 + {{{Z_2}} \over {{Z_1}}}}}1+Z1​Z2​​q​
  2. B
    q1+Z1Z2{q \over {1 + {{{Z_1}} \over {{Z_2}}}}}1+Z2​Z1​​q​
  3. C
    qZ2Z1q{{{Z_2}} \over {{Z_1}}}qZ1​Z2​​
  4. D
    qZ1Z2q{{{Z_1}} \over {{Z_2}}}qZ2​Z1​​
View written solutionFree

Correct answer: A

  1. Use the law of electrolysis

    The mass deposited in a voltmeter is given by m=ZQm = ZQm=ZQ where ZZZ is the electrochemical equivalent and QQQ is the charge passed.

  2. Let charges through copper and silver voltmeters be

    • Copper voltmeter: q1q_1q1​
    • Silver voltmeter: q2q_2q2​

    Since they are connected in parallel, the total charge is q1+q2=qq_1 + q_2 = qq1​+q2​=q

  3. Condition of equal masses deposited

    Given that equal masses of copper and silver are deposited, mCu=mAgm_{\text{Cu}} = m_{\text{Ag}}mCu​=mAg​

    Using m=ZQm = ZQm=ZQ, Z1q1=Z2q2Z_1 q_1 = Z_2 q_2Z1​q1​=Z2​q2​

  4. Express q1q_1q1​ in terms of q2q_2q2​

    q1=Z2Z1q2q_1 = \frac{Z_2}{Z_1} q_2q1​=Z1​Z2​​q2​

  5. Substitute into total charge equation

    q1+q2=qq_1 + q_2 = qq1​+q2​=q Z2Z1q2+q2=q\frac{Z_2}{Z_1}q_2 + q_2 = qZ1​Z2​​q2​+q2​=q

    q2(1+Z2Z1)=qq_2\left(1 + \frac{Z_2}{Z_1}\right) = qq2​(1+Z1​Z2​​)=q

  6. Charge through silver voltmeter

    Therefore, q2=q1+Z2Z1q_2 = \frac{q}{1 + \frac{Z_2}{Z_1}}q2​=1+Z1​Z2​​q​

  7. Match with options

    This corresponds to Option A.

Final Answer: q1+Z2Z1\boxed{\frac{q}{1 + \frac{Z_2}{Z_1}}}1+Z1​Z2​​q​​

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