Question

if L be the inductance,R resistance and C be the capacitance of the capacitor then dimensional formula of L/R and RC are​

Answer 1

dimensional formula of L/R = [T]

dimensional formula of RC = [T²]

L is the inductance, R is the resistance and C is the capacitance.

it's hard to remember dimensional of each term so let's derive them by their usual formula.

we know, U = 1/2 Li²

where U is energy, L is inductance and I is current.

so, dimension of L = dimension of {U/i²}

= [ML²T-²]/[A²]

= [ML²T-²A-²]

we also know, U = i²Rt

so, dimension of R = dimension of {U/i²t}

= [ML²T-²]/[A²T]

= [ML²T-²A-²T-¹]

now use formula, U = Q²/2C

so, dimension of C = dimension of {Q²/U}

= [A²T²]/[ML²T-²]

= [M-¹L-²T⁴A²]

dimensional formula of L/R = [ML²T-²A-²]/[ML²T-²A-²T-¹] = [T]

dimensional formula of RC = [ML²T-²A-²T-¹][M-¹L-²T⁴A²] = [T²]

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Answer 2

$\huge\bold\purple{Answer:-}$

If L be the inductance, R resistance and C be the capacitance of a capacitor, then dimensional formulae of L/R and RC are. (D) M0L0T,M0L0T.