Question

two conducting rods A and B of same length and cross sectional area are connected 1. inseries 2. in parallel . in both combination temperature difference of 100^o C is maintained. if K₁=3K&K₂= K then the ratio of heat current flowing in parallel to series combination is
1.16/3
2.3/16
3.1/1
4.1/3

Answer 1

The rate of heat transfer is given by $\frac{dQ}{dt}=\frac{kA∆T}{l}$. Now series the conductivity will be $\frac{K_1{K}_2}{K_1+K_2}=\frac{3k^2}{4k}=\frac{3}{4}k$ and for parallel connection the conductivity will be $K_1+k_2=4k$. No we can see from the conduction equation that the heat transfer is proportion to the conductivity, so the ratio will be equal to the ratio of the conductivity which is $\frac{{\displaystyle \frac{3}{4}}}{4}=\frac{3}{16}$