Correct Answer - Option 4 : R < 2
\(\sqrt{L/C}\)
Concept:
The characteristic equation of a series RLC circuit is given as –
\({s^2} + \frac{R}{L}s + \frac{1}{{LC}} = 0\) ---(1)
Calculation:
Comparing eq. (1) with the standard 2nd order equation is
\({s^2} + 2\xi {ω _n}s + ω _n^2 = 0\)
We get, \({ω _n} = \frac{1}{{\sqrt {LC} }}\)
2ζωn = R/L
\(2ζ = \frac{R \sqrt{LC}}{L} = R \sqrt{\frac{C}{L}}\)
For oscillatory, ζ < 1
R < 2 \(\sqrt{L/C}\)
