question_answer

Finding dimensions of resistance R and inductance L, speculate what physical quantities (L/R) and \[\frac{1}{2}L{{I}^{2}}\] represent, where I is current?

Answer:

                The dimensions of R and L are : \[R=\text{ }\left[ {{\text{M}}^{\text{1}}}{{L}^{2}}{{T}^{-3}}{{\text{A}}^{-2}} \right]\]and \[L=[M{{L}^{2}}{{T}^{-2}}{{\text{A}}^{-2}}]\] Now, \[\frac{L}{R}=\frac{M{{L}^{2}}{{T}^{-2}}{{A}^{-2}}}{M{{L}^{2}}{{T}^{-3}}{{A}^{-2}}}={{T}^{1}}\] It represents time constant of RL circuit. Again,      \[\frac{1}{2}L{{I}^{2}}=\left[ M{{L}^{2}}{{T}^{-2}}{{A}^{-2}} \right]\times {{A}^{2}}=\left[ {{M}^{1}}{{L}^{2}}{{T}^{-2}} \right]\] It represents (magnetic) energy stored in an inductor.