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
B
1.6units
C
2.4units
D
2.8units

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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