Problem 2 Obtain the second-order ODE describing the capacitor voltage v(t) in the series RLC circuit...
1) (40 pts total) Solving and order ODE using Laplace Transforms: Consider a series RLC circuit with resistor R, inductor L, and a capacitor C in series. The same current i(t) flows through R, L, and C. The voltage source v(t) is removed at t=0, but current continues to flow through the circuit for some time. We wish to find the natural response of this series RLC circuit, and find an equation for i(t). Using KVL and differentiating the equation...
Consider the series RLC circuit in Figure 1. Suppose the source voltage is initially OV, and no energy is stored in both the capacitor and inductor. At t = 0, the source voltage is switched to 1V. Calculate the resistor, inductor and capacitor voltages, and the loop current V (t),,(t),Vc(t),i(t). Show all the steps. C1 L1 1.2u 8.2m 10 3 R1 Figure 1: A series RLC circuit
An RLC series circuit has a voltage source given by E(t)= 20 V, a resistor of 245 Q, an inductor of 7 H, and a capacitor of 0.05 F. If the initial current is zero and the initial charge on the capacitor is 9 C, determine the current in the circuit for t> 0. |(t) = (Type an exact answer, using radicals as needed.)
Solve it as shown but use these values instead: An RLC series circuit has a voltage source given by E(t)=10 V, a resistor of 175 Ω, an inductor of 5 H,and a capacitor of 0.01 F. If the initial current is zero and the initial charge on the capacitor is 8 C, determine the current in the circuit for t>0. An RLC series circuit has a voltage source given by E(t) = 20 V, a resistor of 140 2, an...
2-a)-RLC components connected in series in a circuit supplied by a variable dc voltage can be described by the following differential equations: di(t) wherei@ is the loop current and V1(t) İs the voltage drop across the inductor.+' The voltage drop across the resistor is given by Ohm's law vR(t) R i(t) and the voltage drop across the capacitor vc(t) is given by i(t) dt For a series circuit ye)t vit)t velt) v(t) where v(t) is applied voltage: Figure 3: RLC...
Exercise 3 An RLC circuit is made of a resistor, an inductor and a capacitor connected in series to a battery. The current I(t) in such a circuit satisfies the ODE LI"(t) + RI (1) + (t) = G(t) where L is the inductance (unit: henrys (H)), R is the resistance (unit: ohms (N2), C is the capacitance (unit: farads (F)), and G is the forcing term generated by an AC power (G is actually the derivative with respect to...
An RLC circuit has an initial voltage across the capacitor and polarity as marked on the circuit shown below. The switch is closed at t = 0 and a current i(t) is assumed to flow clockwise in the circuit. Determine which expression correctly represents the Laplace-transformed value of current, i(s). Note that the coefficient of the highest power of s in the denominator may have to be made unity. (TCO 2) An RLC circuit has an initial voltage across the...
Question 2 (5 marks) In a single-loop LRC-series circuit, Kirchhoffs second law states that the sum of voltage drops across an inductor, capacitor, and resistor is equal to the impressed voltage E(t). Use the Laplace trans form to find the charge on the capacitor in an RLC-series circuit at t 10 s when Lh, R 20, C = f, q(0) = 2 C, i (0) = 0 A, E(t) (10 0 st<5 t 5 Question 2 (5 marks) In a...
Consider the series RLC circuit in Figure 1. Suppose the source voltage is initially OV, and no energy is stored in both the capacitor and inductor. At t = 0, the source voltage is switched to 1V. Calculate the resistor, inductor and capacitor voltages, and the loop current VROV.O.Vc),it). Show all the steps. SOL L1 n 8.2m 10 3 R1 Figure 1: A series RLC circuit
A sinusoidal voltage v(t) = (40 V) sin(100t) is applied to a series RLC circuit with L = 160 mH, C = 99 mu/F. and R = 68 ohm. What is the impedance of the circuit? What is the current amplitude? Determine the numerical values for I_m, and omega, and phi in the equation i(t) = I_m sin(omegst minus phi).