Question #230620

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 â€“ sign for a negative integer)

Expert's answer

Using Kirchoff voltage law

"V(s)=I(s)(R+sL+\\frac{1}{sC})\\\\\nV(s)=I(s)(6+s100\\times{10^{-3}}+\\frac{1}{s588\\times{10^{-6}}})\\\\\n\\dfrac{I(s)}{V(s)}=\\dfrac{1}{6+0.1s+\\frac{1700.7}{s}}\\\\\n\\dfrac{I(s)}{V(s)}=\\dfrac{60s}{s^2+60s+102040.8}\\\\\nPoles\\\\\ns^2+60s+102040.8=0\\\\\ns_{1,2}=\\dfrac{-60\\pm\\sqrt{60^2-4(1)(102040.8)}}{2(1)}\\\\\ns_{1,2}=\\dfrac{-60\\pm636.1j}{2(1)}\\\\\ns_1=\\dfrac{-60+636.1j}{2}\\\\\ns_1=-30+218.02j\\\\"

x location is the Real part

Therefore, answer is -30.0rad\sec

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