Question

Six identical conducting rods are joined as shown in the figure. Points A and D are maintained at temperatures ${200}^{o}C$ and $20{}^{o}C$ respectively. The temperature of junction B will be

• A. $120{}^{o}C$
• B. $100{}^{o}C$
• C. $140{}^{o}C$
• D. $80{}^{o}C$

Answer 1

The correct option is C $140{}^{o}C$

Let the thermal resistance of each rod be $R$.

The two resistances connected along two paths from B to C are equivalent to $2R$ each and their parallel combination is $R$.
Effective thermal resistance between B and D = $2R$

Temperature of interface, $\theta =\frac{R_1{\theta }_2+R_2{\theta }_1}{R_1+R_2}\theta =\frac{R\times 20+2R\times 200}{R^{}+2R^{}}=\frac{420}{3}=140{}^{o}C$