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Two metal wires of identical dimensions are connected in series. If \sigma _1 and \sigma _2 are the conductivities of the metal wires respectively, the effective conductivity of the combination is :

Option: 1

\frac{{\sigma _1 + \sigma _2 }} {{2\sigma _1 \sigma _2 }}


Option: 2

\frac{{\sigma _1 + \sigma _2 }} {{\sigma _1 \sigma _2 }}


Option: 3

\frac{{\sigma _1 \sigma _2 }} {{\sigma _1 + \sigma _2 }}


Option: 4

\frac{{2\sigma _1 \sigma _2 }} {{\sigma _1 + \sigma _2 }}


Answers (1)

best_answer

 

In Series Combination -

R_{eq}=R_{1}+R_{2}+R_{3}---------R_{n}

- wherein

Req= equivalent thermal resistance

 

 In series combination 

Resistance R_{eq}=R_1+R_2

R=\frac{L}{KA} \Rightarrow R_1=\frac{L}{\sigma _1A}

R_2=\frac{L}{\sigma _2A}

R_{eq}=\frac{2L}{\sigma _{eq}A}=\frac{L}{\sigma _1A}+ \frac{L}{\sigma _1A}

OR =\frac{2}{\sigma _{eq}}=\frac{\sigma _1 +\sigma _2}{\sigma_1\sigma_2}

OR {\sigma _{eq}}=\frac{2\sigma _1 \sigma _2}{\sigma_1+\sigma_2}

Posted by

Irshad Anwar

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