Question

Four rods of same material having the same cross section and length have been joined as shown. The temperature of the junction of the rods will be

• A. ${20}^{\circ }\text{C}$
• B. ${30}^{\circ }\text{C}$
• C. ${45}^{\circ }\text{C}$
• D. ${60}^{\circ }\text{C}$

Answer 1

The correct option is C ${45}^{\circ }\text{C}$

$i_{in}=i_{out}$

$i=\frac{dQ}{dt}=\frac{\Delta T}{R}$

$R=\frac{l}{kA}$


$i_{in}=i_{out}$

$i_3+i_4=i_1+i_2$

$\frac{60-T}{R_3}+\frac{90-T}{R_4}=\frac{T-O}{R_1}+\frac{T-30}{R_2}$
$⟹(60-T)+(90-T)=(T-0)+(T-30)$
$150-2T=2T-30$
$T={45}^{0}C$