4. Consider the following RLC circuit, whereL = 1H, R = 50, C = 250mF. Vgen = 10t-10. Thereis initial charge on the capacitor as q(0) = 2.5Coulumb. The switch has been open for a long time andcloses at t = 0.a) Write the differential equation describing the current inthe circuit for t> 0.b) What are the initial values for current, i.e., [(0) and i'(0)?c) Write the characteristic equation and identify the type of the circuit (overdamped.underdamped, or critically damped).O

Answered: Image /qna-images/answer/f66c7f17-4bd6-4f10-8980-ca26e28f6473.jpg

Answered: 4. Consider the following RLC circuit,…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Similar questions

Consider the RLC circuit shown where the initial current flowing through the circuit at time t = 0 is I_0 = 5 and the initial charge on the capacitor at time t = 0 is Q_0 = 2. The components have values of R = 100 ohms, L = 5 H, and C = 1/450,500 F. Write the differential equation for Q(t), the charge across the capacitor, assuming the voltage source V(t) = 0
An RLC circuit connected in series has a resistance of 5 ohms, an inductance of0.05 henry, a capacitor of 4 x 10-4farad, and an applied alternating emf of200cos100t volts. Find an expression for the current flowing through this circuit ifthe initial current and initial charge of the capacitor are both zero.
Assume that the circuit in the image has been connected for a very long time. (a) As time approaches infinity, what wtll happen to the capacitor and inductor? (b) From your answer in (a), draw the equivalent circuit (label appropriately).(c) From your circuit in (b), determine the "steady-state" or "final" values of Vc, lc, IL and VL
Consider the circuit on the left. DC voltage u1(t ≥ 0) = U is applied at time t = 0. Both meshes must include the input voltage. At time t = 0, the capacitors are free of energy. The following applies: τ = R*C. Derive the 2nd order differential equation for the capacitor voltage u2(t).
The resistance, inductance, and capacitance in a parallel RLC circuit are 1900 ohms, 240 mH, and 15 nF,respectively. a) Calculate the roots of the characteristic equation that describe the voltage response ofthe circuit. b) Will the response be over-, under-, or critically damped? c) What value of R will yield adamped frequency of 12 krad/s ? d) What are the roots of the characteristic equation for the value of Rfound in (c)? e) What value of R will result in a critically damped response?
The resistance, inductance and capacitance in a parallel RLC circuit are 1500 ohms, 400mH and 10nF, 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 C will yield a damped frequency of 15 krad/s? d. What are the roots of the characteristic equation for the value of C found in (c)? e. What value of C will result in a critically damped response?
A RL circuit has an emf of 5 volts, a resistance of 50 ohms, an inductance of 1 henry, and no initial current. Find (a) the current in the circuit at any time t and (b) its steady-state component.
Make the equation s(s+1)(s+2)+K=0 in the form of 1+KF(s) and explain the drawing of root-locus curves. (Note: Indicate the splitting points, centers and angles of the asymptotes)
The circuit elements in the circuit L=50 mH, and C=0.2 μF. The initial inductor current is−45 mA and the initial capacitor voltage is 15 V. The resistance is increased to250 Ω. Find the expression for v(t) for t≥0.
I'm working on a circuit design problem where I need to find the values for an RLC circuit that, when placed in parallel with a 100 Ohm resistor, results in an admittance of 28.627 /_ -31.900 mS at 100 Hz. I've successfully calculated the resistance (R = 33 Ohm) and inductance (L = 55 mH), which are correct, but am having trouble with the capacitance C. My attempts to calculate C using the capacitive reactance Xc consistently lead me to 0.02 mF, which isn't accepted as correct. The impedance I've calculated for the RLC network is Z_RLC = 33 + j34.9 Ohm. Could you help me verify the Xc calculation and find the correct value for C in mF? Thank you!
The resistance, inductance and capacitance in a parallel RLC circuit are 2000 ohms , 250mH and 10nF respectivalya) Calculate the roots of the characteristic eqaution that describe the voltageresponse of the circuitb) Will the response be over, under or critically damped?c) What value of the R will yield a damped frequency of 12 krad/s?d) What are the roots of characteristic equation for the value R found in c?e) What value of R will result in a critically damped response?
A series RC circuit with R = 40Ω and C = 0.1F is connected to a sinusoidal voltage v = 180sin(20t + β)V source at a time where β = 90°. The capacitor is initially uncharged. The s-domain equation for the current is given by the attached picture. Find the value of K1, K2, and K4.

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