Question

Two identical square rods of metal are welded end to end as shown in the figure $(1)$ , $20cal$ of heat flows through it in $4min$ . If the rods are welded as shown in the figure $(2)$ , the same amount of heat will flow through the rods in

• A. $1min$
• B. $2min$
• C. $4min$
• D. $16min$

Answer 1

Answer: (A)

Figure (1) $\to$ series combination
Figure (2) $\to$ parallel combination
Thermal resistance for each block to be $\text{R}$
Then
Thermal resistance for the case I ${\text{R}}_1=2\text{R}$
Thermal resistance for the case II ${\text{R}}_2=\text{R}\text{/2}$
Thermal resistance for case II
${\text{I}}_1=\frac{\Delta \text{T}}{{\text{R}}_1}$ ${\text{I}}_2=\frac{\Delta \text{T}}{{\text{R}}_2}$
$\Rightarrow 4{\text{I}}_1={\text{I}}_2$
$4\frac{\Delta Q_1}{\Delta {\text{t}}_1}=\frac{\Delta Q_2}{\Delta {\text{t}}_2}if\Delta Q_1=Q_2$
then
$4\Delta {\text{t}}_2=\Delta {\text{t}}_1$
$\Delta {\text{t}}_2=\Delta {\text{t}}_1/4=\frac{4}{4}=1min$