Question

8.1 The resistance, inductance, and capacitance in a parallel RLC circuit are 1 kN, 12.5 H, and 2 uF, respectively. a. Calculate the roots of the characteristic equation that describe the voltage response of the circuit. b. Will the response be over-, under-, or critically damped? c. What value of R will yield a damped frequency of 120 rad/s? d. What are the roots of the characteristic equation for the value of R found in (c)? e. What value of R will result in a critically damped response?

Answer 1

to af Apply laplace transform The circuit Vas Apply nodal analyn – 161+ Yes Yes Vasil + Es+cs) = 1681 U(S) rces'+25 +R] = RIS 2014 Vila VS ICS! sit the state : characteristic Equation ů Šta ste :0-0 put the values siet visiemso vest = 0 5 + 5005 + 40,000 20 - S. : -100, - 400 6) wr= 40000 = Wn= 200r.d/sec 2&wn = 500 = &= 500 2X200 sa 1:25 > over damped system c) from o compare with 5²+2&wast was o I was the =) Wn the

2&wn = e =) & = 2n the & ză Given wa= to rad/sec - ۱ ) له = ده 5x24 wie wil-ww & ☺ wat so = 40,000 wildl= (he) = REW wy&= 6.25X1000 • franco 1201 += 40.000 - 6. oktober 6.25X10" 25600 d) from o [R = 1562.50 5++ 3205 + 49000=0 ... 5,2 = (-160 I j120) el critically damped means &=1 : &' a T 681) Ratri Pertama (R = 1250

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