Question

A series RLC circuit has a resistance of 6.0 ohm, a capacitance of 5882 microfarads, and an inductance of 100 millihenries. What is the x location in rad/sec of the pole s1 ? (Type in a one-decimal number, make sure to use the – sign for a negative integer)

Answer 1

Using Kirchoff voltage law

$V(s)=I(s)(R+sL+\frac{1}{sC})\\ V(s)=I(s)(6+s100\times{10^{-3}}+\frac{1}{s588\times{10^{-6}}})\\ \dfrac{I(s)}{V(s)}=\dfrac{1}{6+0.1s+\frac{1700.7}{s}}\\ \dfrac{I(s)}{V(s)}=\dfrac{60s}{s^2+60s+102040.8}\\ Poles\\ s^2+60s+102040.8=0\\ s_{1,2}=\dfrac{-60\pm\sqrt{60^2-4(1)(102040.8)}}{2(1)}\\ s_{1,2}=\dfrac{-60\pm636.1j}{2(1)}\\ s_1=\dfrac{-60+636.1j}{2}\\ s_1=-30+218.02j\\$

x location is the Real part

Therefore, answer is -30.0rad\sec