The responses of a series RLC circuit are vC t 40 40e 20t

The responses of a series RLC circuit are v_C (t) = 40 - 40e ^-20t + 30_e^-50t V i_L(t) = 480 _e^-20t - 900e ^-50t mA where v_c and i_L are the capacitor voltage and inductor current, respectively. Determine the values of R. L. and C. Please express R in ohms, L in henrys. and C in microfarads. Round the final answers to two decimal places, if necessary. R = Ohm L = H C = mu F

Solution

BY APPLYING LAPLACE TRANSFORMATION

i_l(s)=480/s+20 -900/s+50

v_l(s)=40/s -40/s+20 +30/s+50

FOR CAPACITOR I_c(t)=Cdv(t)/dt given circuit is series circuit hence I_C(t)=I_l(t)

by solving above equations we will get the results

by taking final conditions at t=infinity inductor acts as a short circuit and capacitor acts as a open circuit

then V_c(t)=40v which is source voltage

by taking intial conditions at t=0 inductor acts as a open circuit and capacitor acts as a short circuit

the voltage across the indictor is same as source voltage

by solving above equations we will get inductor value

from inductor value and cuurent inductance votage will be found

from source voltage inductor voltage and capacitor volage the resistor voltage will be found. from that resistance can be found.