Question

Two identical rectangular rods of metal of thermal resistance R, are welded end to end as shown
in figure (i) and 10 J of heat flows through the rods in 2 min. How long would it take for 30 J of
heat to flow through the rods if they are welded as shown in figure (ii)

• A. 2 min
• B. 1.5 min
• C. 1 min
• D. 4 min

Answer 1

The correct option is B 1.5 min

The thermal resistance of each rod is R.
In case (i) the rods are in series.
$\therefore$ $R_s$ = R + R = 2R
Rate of flow of heat will be
$\frac{dQ}{dt}=\frac{\Delta T}{R_s};\frac{10}{2}=\frac{(100-0)}{2R}\therefore R=10$
In case (ii) the rods are parallel; so
$\frac{I}{R_p}=\frac{I}{R}+\frac{I}{R}\Rightarrow R_p=\frac{R}{2}=5$
Now, rate of flow of heat in this case will be
$\frac{dQ}{dt}=\frac{\Delta T}{R_p}\Rightarrow \frac{30}{t}=\left[\frac{100-0}{5}\right]$
Or t = 1.5 minute.