A) Dimensional formula of thermal conductivity \[\left( K \right)\] is \[{{M}^{1}}{{L}^{1}}{{T}^{-3}}{{K}^{-1}}\].
B) Dimensional formula of potential \[\left( V \right)\], \[{{M}^{1}}{{L}^{1}}{{T}^{-2}}{{A}^{-1}}\].
C) Dimensional formula of permeability of free space \[({{\mu }_{0}})\] is \[{{M}^{1}}{{L}^{1}}{{T}^{-2}}{{A}^{-2}}\]
D) Dimensional formula of \[RC\]is \[{{M}^{0}}{{L}^{0}}{{T}^{-1}}\].
Correct Answer: B
Solution :
: Thermal conductivity \[=\frac{Heat\text{ }energy\times thickness}{Area\times Temperature\times time}\] \[[K]=\frac{[M{{L}^{2}}{{T}^{-2}}][L]}{[{{L}^{2}}][K][T]}=[{{M}^{1}}{{L}^{1}}{{T}^{-3}}{{K}^{-1}}]\] \[Potential=\frac{Work}{\text{Charge}}\] \[[V]=\frac{M{{L}^{2}}{{T}^{-2}}}{[AT]}=[{{M}^{1}}{{L}^{2}}{{T}^{-3}}{{A}^{-1}}]\] Permeability of free space \[=\frac{2\pi \times force\times \text{distance}}{curent\times curent\times lenght}\] \[[{{\mu }_{0}}]=\frac{[{{M}^{0}}{{L}^{0}}{{T}^{0}}][ML{{T}^{-2}}][L]}{[A][A][L]}=[{{M}^{-1}}{{L}^{1}}{{T}^{-2}}{{A}^{-2}}]\]RC is the time constant of RC circuit. \[[RC]=[{{M}^{0}}{{L}^{0}}{{T}^{-1}}]\]
You need to login to perform this action.
You will be redirected in
3 sec
