Finding dimensions of resistance R and indcutance L, speculate what physcial quantities `(L//R) and (1)/(2)LI^2` represent, where I is current?

Explanation

As `e=L (di)/(dt)` i.e., `L=e (dt)/(di)`
So, `[L]=[W/q][t/i] rarr [(ML^(2)T^(-2))/(AT)xxT/A]`
i.e., `[L]=[ML^(2)T^(-2)A^(-2)]`
and as `V=IR" "`i.e., `R=V//I`
So, `[R]=[W/(qA)]rarr[(ML^(2)T^(-2))/(ATA)]`
i.e., `[R]=[ML^(2)T^(-3)A^(-2)]`
So, `[L/R]=[(ML^(2)T^(-2)A^(-2))/(ML^(2)T^(-3) A^(-2))]=[1/T^(-1)]=[T]`
and `[1/2 Li^(2)]=[ML^(2)T^(-2)A^(-2)][A^(2)]=[ML^(2)T^(-2)]`
Now as `(L//R)` has dimensions of time and so is called time constant of `L-R` circuit and `(1//2)Li^(2)` has dimensions of work or energy, so it represents magnetic energy stored in a coil.
Note : (i) In case of object questions the units and dimensions of `(L//R)`, CR or LC can be calculated easily as follows:
(a) `L/R rarr ("henry")/(ohm)=(ohm xx s)/(ohm) rarr s rarr [T]`
(b) `CR rarr` farad `xx` ohm `rarr ("coul")/("volt")xx("volt")/("amp") rarr s rarr [T]` [as amp = coul/s]
(c) `sqrt(LC) rarr sqrt("henry"xx"farad")=sqrt(ohmxxsxx("coul")/("volt")) rarrsqrt(("volt")/(amp)xx("coul")/("volt")xxs)rarrsrarr [T]`
(ii) Similarly units and dimensions of `i^(2) Rt, (1//2)CV^(2)` or `(1//2)Li^(2)` are of work of energy, i.e., `[ML^(2)T^(-2)]`.