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. $2.8units$

Answer 1

The correct option is A $1.2units$

When the resistors are connected in series the equivalent resistance is

$R=R_1+R_2+R_3$

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

$so,$

$\rho ={\rho }_1+{\rho }_2+{\rho }_3$

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

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

$\frac{1}{\sigma }=\frac{1}{{\sigma }_1}+\frac{1}{{\sigma }_2}+\frac{1}{{\sigma }_3}$

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

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

$\sigma =1.2units$