A) \[[M{{L}^{-2}}TK]\]
B) \[[{{M}^{-1}}{{L}^{-2}}TK]\]
C) \[[M{{L}^{-\,2}}{{T}^{-\,3}}K]\]
D) \[[{{M}^{-1}}{{L}^{-\,2}}{{T}^{3}}K]\]
Correct Answer: D
Solution :
| Electrical resistance, \[R=\frac{V}{I}\] |
| So, heat resistance or thermal resistance is |
| \[{{R}_{Th}}=\frac{\Delta T}{\Delta Q}\] |
| where, \[\Delta T=\] temperature difference and \[\Delta Q=\] heat flow rate \[=\frac{H}{t}.\] |
| \[\therefore \]\[{{R}_{Th}}=\frac{\Delta T}{\left( \frac{KA\Delta T}{l} \right)}\]\[\Rightarrow \]\[{{R}_{Th}}=\frac{l}{KA}\] |
| So, its dimensions are |
| \[[{{R}_{Th}}]=\frac{[L]}{[ML{{T}^{-\,3}}{{K}^{-1}}{{L}^{2}}]}=[{{M}^{-\,1}}{{L}^{-\,2}}{{T}^{3}}K]\] |
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