Question

If l and r denote inductance and resistance.then the dimebsion of l/r is

Answer 1

First of all we have to find out dimension of L and R .
We know, relation L answer energy is E = 1/2Li²
so, dimension of L = dimension of energy/dimension of i²
= [ML²T⁻²]/[A²] = [ML²T⁻²A⁻²]

Similarly we know, relation between R and energy is E = i²Rt
So, dimension of R = dimension of E/dimension of i²t
= [ML²T⁻²][A²T] = [ML²T⁻³A⁻²]

Now, dimension of L/R = dimension of L/dimension of R
= [ML²T⁻²A⁻²][ML²T⁻³A⁻²] = [T]

Hence, answer is [T]