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10th Class Science Electricity and Circuits Question Bank Electricity

  • question_answer
    The resistors \[{{R}_{1}},{{R}_{2}},{{R}_{3}}\] and \[{{R}_{4}}\] in the given circuit are all equal in value and connected with a negligible resistance wire. Which of the following is correct relationship between the voltmeters readings \[{{V}_{1}},{{V}_{2}}\] and \[{{V}_{3}}\]

    A) \[{{V}_{1}}={{V}_{2}}={{V}_{3}}\] 

    B) \[{{V}_{1}}={{V}_{2}}>{{V}_{3}}\] 

    C) \[{{V}_{1}}<{{V}_{2}}<{{V}_{3}}\] 

    D) \[{{V}_{1}}={{V}_{2}}<{{V}_{3}}\]

    Correct Answer: D

    Solution :

    Total potential difference across resistances is \[V={{V}_{1}}+{{V}_{2}}+{{V}_{3}}\] Since the resistances are connected in series, the same current flow through each resistance and\[{{R}_{1}}={{R}_{2}}={{R}_{3}}=R\] \[\therefore \] \[{{V}_{1}}=l{{R}_{1}}=lR\] \[{{V}_{2}}=l{{R}_{2}}=lR\] \[{{V}_{3}}=l({{R}_{3}}+{{R}_{4}})=l(R+R)=2lR\] \[\therefore \] \[{{V}_{1}}={{V}_{2}}<{{V}_{3}}\]


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