An RLC-circuit consists of a resistor (resistance R ohms), capacitor (capacitanc

Question

An RLC-circuit consists of a resistor (resistance R ohms), capacitor (capacitance C farads), and inductor (inductance L henries) in series. In the absence of applied voltage, the current y (t) in the circuit satisfies the DE L d2y / dt2 + R dy / dt + y / c = 0. For the circuit parameters R = 0.5 kohm, C = 1.0 muF, and L = 200 mH, show that ringing occurs and find its radian frequency (in Hz). The symbols kohm, muF, and mH refer to 103 ohms, 10-6 farads, and 10"3 henries, respectively. (For R and C and L in ohms and farads and henries, the units for R C and LC are respectively sec and sec2.) For the L, C-values in (a), critical damping will occur at what value of the resistance R?

Explanation / Answer

LS^2 Y(S)+RSY(S)+ 1/C Y(S)=0 Y(S)(LS^2 + RS+1/C)=0 LS^2 + RS+1/C=0 S=jw -Lw^2+JWR=1/C=0 -0.2w^2+500JW+10^6=0 SOLVE FOR W THE U GET FREQ

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