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  4. Let L denote self inductance of a coil which is in series with a capacitor of capacitance C. Which of the following has unit of second ?

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Q. Let L denote self inductance of a coil which is in series with a capacitor of capacitance C. Which of the following has unit of second ?

KCETKCET 1995Physical World, Units and Measurements

Solution:

[L] = $[ML^2T^{-2}A^{-2}]$
[C] = $[M^{-1}L^{-2}T^4 A^2] $
$\therefore [LC] = [T^2] \therefore [\sqrt{LC}] = [T]$
$f = \frac{1}{T} = \frac{1}{2 \pi \sqrt{LC}}$
$\therefore [T] = [\sqrt{LC}]$