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Question

Three metal rods of same lengths and same area of cross- section having conductivies $$1,2,3$$ units are connected in series. Then their effective conductivity will be. 


A
1.2units
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B
1.6units
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C
2.4units
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D
2.8units
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Solution

The correct option is A $$1.2 units$$

When the resistors are connected in series the equivalent resistance is

$$ R={{R}_{1}}+{{R}_{2}}+{{R}_{3}} $$

$$ \because R=\rho \dfrac{l}{A} $$

$$ so, $$

$$ \rho ={{\rho }_{1}}+{{\rho }_{2}}+{{\rho }_{3}} $$

$$ \because \sigma =\dfrac{1}{\rho } $$

Where, $$\sigma $$ and $$\rho $$ are conductivity and resistivity respectively. So,

$$ \dfrac{1}{\sigma }=\dfrac{1}{{{\sigma }_{1}}}+\dfrac{1}{{{\sigma }_{2}}}+\dfrac{1}{{{\sigma }_{3}}} $$

$$ \dfrac{1}{\sigma }=\dfrac{1}{1}+\dfrac{1}{2}+\dfrac{1}{3} $$

$$ \dfrac{1}{\sigma }=\dfrac{5}{6} $$

$$ \sigma =1.2\,units $$


Physics

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