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Addition of Vectors

If TA and ...

Question

If $T_{A}$ and $T_{B}$ are the temperature drops across the rod $A$ and $B$ , then

A

\frac{T_{A}}{T_{B}} = \frac{3}{1}

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B

\frac{T_{A}}{T_{B}} = \frac{1}{3}

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C

\frac{T_{A}}{T_{B}} = \frac{3}{4}

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D

\frac{T_{A}}{T_{B}} = \frac{4}{3}

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Solution

The correct option is A $\frac{T_{A}}{T_{B}} = \frac{1}{3}$
The heat flowing through a rod is given by:
$˙ Q = K A \frac{Δ T}{l}$
Here the rods are in series, i.e. the rods have the same heat flowing through them.
$3 K A \frac{T_{A}}{l} = K A \frac{T_{B}}{l}$
i.e.
$\frac{T_{A}}{T_{B}} = \frac{1}{3}$

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