Question
The dimensions of coefficient of self inductance are
A.
$$\left[ {M{L^2}{T^{ - 2}}{A^{ - 2}}} \right]$$
B.
$$\left[ {M{L^2}{T^{ - 2}}{A^{ - 1}}} \right]$$
C.
$$\left[ {ML{T^{ - 2}}{A^{ - 2}}} \right]$$
D.
$$\left[ {ML{T^{ - 2}}{A^{ - 1}}} \right]$$
Answer :
$$\left[ {M{L^2}{T^{ - 2}}{A^{ - 2}}} \right]$$
Solution :
Energy stored in an inductor, $$U = \frac{1}{2}L{I^2}$$
$$\eqalign{
& \Rightarrow L = \frac{{2U}}{{{I^2}}} \cr
& \therefore \left[ L \right] = \frac{{\left[ {M{L^2}{T^{ - 2}}} \right]}}{{{{\left[ A \right]}^2}}} \cr
& = \left[ {M{L^2}{T^{ - 2}}{A^{ - 2}}} \right] \cr} $$