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Two rods of same length and material are joined end to end. They transfer heat in 8 second. When they are joined in parallel they transfer same amount of heat in same conditions in time
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Verified Answer
The correct answer is:
2 s
Let $R$ be the thermal resistance of each rod when connected in series, the total resistance will be $\mathrm{R}_{\mathrm{s}}=2 \mathrm{R}$
Whey they are connected in parallel, the effective resistance will be
$$
\begin{aligned}
& \mathrm{R}_{\mathrm{p}}=\frac{\mathrm{R}}{2} \\
& \therefore \frac{\mathrm{R}_{\mathrm{p}}}{\mathrm{R}_{\mathrm{s}}}=\frac{1}{4}
\end{aligned}
$$
In parallel combination, the resistance becomes one-fourth and hence time will also become one-fourth.
$\therefore$ Time taken $\frac{8}{4}=2 \mathrm{~s}$
Whey they are connected in parallel, the effective resistance will be
$$
\begin{aligned}
& \mathrm{R}_{\mathrm{p}}=\frac{\mathrm{R}}{2} \\
& \therefore \frac{\mathrm{R}_{\mathrm{p}}}{\mathrm{R}_{\mathrm{s}}}=\frac{1}{4}
\end{aligned}
$$
In parallel combination, the resistance becomes one-fourth and hence time will also become one-fourth.
$\therefore$ Time taken $\frac{8}{4}=2 \mathrm{~s}$
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