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Current Electricity question

2015 · Q113
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Current Electricity question

2015 · Q113

NEETPhysicsCurrent ElectricityMCQ+4 / −1
Two metal wires of identical dimensions are connected in series. If σ\sigmaσ1 and σ\sigmaσ2 are the conductivity of the combination is
  1. A
    σ1+σ2σ1σ2{{{\sigma _1} + {\sigma _2}} \over {{\sigma _1}{\sigma _2}}}σ1​σ2​σ1​+σ2​​
  2. B
    σ1σ2σ1+σ2{{{\sigma _1}{\sigma _2}} \over {{\sigma _1} + {\sigma _2}}}σ1​+σ2​σ1​σ2​​
  3. C
    2σ1σ2σ1+σ2{{2{\sigma _1}{\sigma _2}} \over {{\sigma _1} + {\sigma _2}}}σ1​+σ2​2σ1​σ2​​
  4. D
    σ1+σ22σ1σ2{{{\sigma _1} + {\sigma _2}} \over {2{\sigma _1}{\sigma _2}}}2σ1​σ2​σ1​+σ2​​
View written solutionFree

Correct answer: C

In figure, two metal wires of identical dimension are connected in series

AIPMT 2015 Physics - Current Electricity Question 104 English Explanation

Req=1σ1A+1σ2A=leqσeqAeq{R_{eq}} = {1 \over {{\sigma _1}A}} + {1 \over {{\sigma _2}A}} = {{{l_{eq}}} \over {{\sigma _{eq}}{A_{eq}}}}Req​=σ1​A1​+σ2​A1​=σeq​Aeq​leq​​

2lσeqA=1A(σ1+σ2σ1σ2){{2l} \over {{\sigma _{eq}}A}} = {1 \over A}\left( {{{{\sigma _1} + {\sigma _2}} \over {{\sigma _1}{\sigma _2}}}} \right)σeq​A2l​=A1​(σ1​σ2​σ1​+σ2​​)

∴σeq=2σ1σ2σ1+σ2 \therefore {\sigma _{eq}} = {{2{\sigma _1}{\sigma _2}} \over {{\sigma _1} + {\sigma _2}}}∴σeq​=σ1​+σ2​2σ1​σ2​​

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