Two conductors A and B are connected in parallel as shown in Fig.
i. Determine the equivalent thermal resistance.
ii. Determine the heat current in each rod.

Explanation

i. The thermal resistance of the two rods are
`R_A=(l)/(3kA)`,`R_B=(l)/(kA)`
The equivalent resistance is
`(1)/(R )=(1)/(R_A)+(1)/(R_B)=(3kA)/(l)+(kA)/(l)=(4kA)/(l)`
or `R=(l)/(4kA)`
ii. The heat current through each rod is
`I_A=(T_1-T_2)/(R_A)=(100-0)/(l//3kA)=300((kA)/(l))`
`I_B=(T_1-T_2)/(R_B)=(100-0)/(l//kA)=100((kA)/(l))`
Total heat current is
`I=I_A+I_B=400(kA)/(l)`