First slide

Dimensions of physical quantities

Question

The dimensional formula for thermal resistance is

Moderate

A

$[{ML}^{2} T^{- 3} K^{- 1}]$
B

$[{ML}^{2} T^{- 2} K^{- 1}]$
C

$[{ML}^{2} T^{- 3} K^{- 2}]$
D

$[M^{- 1} L^{- 2} T^{3} K]$

Solution

$Heat current = \frac{d Q}{d t} = \frac{TD}{R} H e r e, T D = temperature difference A n d R = thermal resistance = \frac{TD}{d Q / d t} ∴ [R] = [TD] [\frac{d t}{d Q}] = [K] [\frac{T}{{ML}^{2} T^{- 2}}] = [M^{- 1} L^{- 2} T^{3} K]$

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