Question

Three rods of material $x$ and three rods of material $y$ are connected as shown in the figure. All rods are of identical length and cross-section. If the end $A$ is maintained at ${60}^{o}C$ and the junction $E$ at ${10}^{o}C$, find the effective Thermal Resistance. Given the length of each rod = $l$, area of cross-section = $A$, conductivity of $x=K$ and conductivity of $y=2K$.

• A. $\frac{2l}{3KA}$
• B. $\frac{7l}{6KA}$
• C. $\frac{4KA}{3l}$
• D. $\frac{7KA}{3l}$

Answer 1

The correct option is B $\frac{7l}{6KA}$

Since $BCED$ part will act like as wheatstone bridge,so equivalet thermal conductivity is given as follow
$R_{equivalent}=R_{AB}+R_{BE}$
$R_{BE}=\frac{2R\times R}{2R+R}=\frac{2R}{3}$
now $R_{equivalent}=\frac{2R}{3}+\frac{R}{2}=\frac{7R}{6}$
and we know$R=\frac{l}{KA}$
so $R_{equivalent}=\frac{7l}{6KA}$