Question

Two identical square rods of metal are welded end to end as shown in figure (i), 20 calories of heat flows through it in 4 minutes. If the rods are welded as shown in figure (ii), the same amount of heat will flow through the rods in

• A. 1 minute
• B. 2 minutes
• C. 4 minutes
• D. 16 minutes

Answer 1

Answer: (A)

1 minute

Answer 2

$\frac{Q}{t} = \frac{KA\Delta\theta}{l} = \frac{\Delta\theta}{(l/KA)} = \frac{\Delta\theta}{R}$

(R = Thermal resistance)

⇒ $t \propto R$ ($\because$Q and $\Delta\theta$ are same)

⇒ $\frac{t_{P}}{t_{S}} = \frac{R_{P}}{R_{S}} = \frac{R/2}{2R} = \frac{1}{4}$⇒$t_{P} = \frac{t_{S}}{4} = \frac{4}{4} = 1min.$

(Series resistance $R_{S} = R_{1} + R_{2}$ and parallel resistance $R_{P} = \frac{R_{1}R_{2}}{R_{1} + R_{2}}$)