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3. RLC Parallel Circuit a) (7pts) For the circuit shown, determine the ODE relating the voltage...
Exercise 3 An RLC circuit is made of a resistor, an inductor and a capacitor connected...
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...
Derive the ODE for the RLC circuit provided using Kirchoff's voltage and current laws. Indicate the...
Derive the ODE for the RLC circuit provided using Kirchoff's
voltage and current laws. Indicate the order of the equation and
what conditions are required for a unique and completely defined
solution to existing. You should solve for the voltage across the
capacitor as the output, y(t), due to the excitation of the input
voltage, x(t), and the initial conditions, y(0) = c0 and
y'(0)=c1.
Compute the homogeneous solution to the ordinary differential
equation for unknown values of R, L...
3. (40 pts total) Eigenvalues of Systems of Equations Application: Series RLC Circuit, Natural, or Transient...
3. (40 pts total) Eigenvalues of Systems of Equations Application: Series RLC Circuit, Natural, or Transient Response (Remember EE280, maybe not) M SR v(t) Consider a series RLC circuit, with a resistor R, inductor L, and capacitor C in series. The same current i(t) flows through R, L, and C. The switch S1 is initially closed and S2 is initially open allowing the circuit to fully charge. At t=0 the switch S1 opens and S2 closes as shown above. Solving...
use R=1Ω, L=1H and C= 1/5 F Instead (c) In the circuit shown in Figure P2.61(c),...
use R=1Ω, L=1H and C= 1/5 F Instead
(c) In the circuit shown in Figure P2.61(c), x(t) is the input voltage. The voltage y(t) across the capacitor is considered to be the system output wwww L 1H R=20 + y(t) x(t) C (c) Figure P2.61c (i) Determine the differential equation relating x(t) and y(t) (ii) Show that the homogeneous solution of the differential equation from part (i) has the forme "{K\ej2 + K2e"j2r}, and specify the value of a (iii...
Solve for lapalce transform. 3. For the RLC circuit shown in the graph, determine the current...
Solve for lapalce transform.
3. For the RLC circuit shown in the graph, determine the current i (t), taking into account that. i(0) = 0 y 9(0) = 0 L = 1 h, R = 1602, C = 10-4f, E = 20v 00000 L E R
Problem 1 (Problem Solving Workshop 1) For a parallel RL circuit R-10, L 1H Determine 1)...
Problem 1 (Problem Solving Workshop 1) For a parallel RL circuit R-10, L 1H Determine 1) 21 3) 4) The transfer function H(s) = (s), the pole-zero map, and the step response. Let L(0) - OA The state and output equations. Let Lt) be the state variable The block diagram of this system. Let (O) = -1 The response (t) due to a step input (t) = (t) A) using a known software. Problem #2 (Problem Solving Workshop 1) For...
4. (15 points - PA.3) Consider the RLC circuit shown below, where the input and output...
4. (15 points - PA.3) Consider the RLC circuit shown below, where the input and output x(t) and y(t) are the input voltage vi(t) and capacitor voltage vc(t) respectively, and R = 1 K12, C = 0.1 mF, L = 100 H. i(t) + (i) Determine the frequency response of the system H (jw), as well as its magnitude and phase responses. What type of filter does it correspond to? (ii) Sketch its magnitude and phase response in Matlab. You...
HW 2-1. For the RLC circuit in HW 1-2, with the voltage source x(t) as the...
HW 2-1. For the RLC circuit in HW 1-2, with the voltage source x(t) as the 'input' and the loop current y(t) as the 'output' (20 pts) L-11 R=3.22 yo 1) find its frequency response function H(w). (5 pts) 2) then, find its response to the following input signals, respectively 2-a) x(t)=8(t), (2 pts) 2-b) x(t)=u(t), (3 pts) 2-c) x(t)=sin(10t), (3 pts) 2-d) x(t)=2sin(10t)+cos(20t+1), (3 pts) 3) For the signals in 2), calculate the energy or the average power (whichever...
For the circuit shown in Figure 1, determine (a) The transfer function H(s) Vo(s)/V(s) 1 (b)....
For the circuit shown in Figure 1, determine (a) The transfer function H(s) Vo(s)/V(s) 1 (b). The impulse response h(t) given that R,-5Q, R2-2Q, L,-1 mH, and L2 = 2 mH Ri L R2 Figure 1.
TEE301/05 Question 3 (20 marks) An RLC circuit with a 1V DC source is shown in...
TEE301/05 Question 3 (20 marks) An RLC circuit with a 1V DC source is shown in Fig. 1: i(t) Vout - R-0.22 L-0.1 H C- 10 F Fig. 1 (a) List two properties of Laplace transform. Explain these two properties. [6 marks] (b) Assume that the initial inductor current is OA and initial capacitor voltage is 0.4 V 4 marks] (c) Determine the current, t) in time domain by performing inverse Laplace transform. [4 marks) determine the expression of the...
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...
Derive the ODE for the RLC circuit provided using Kirchoff's
voltage and current laws. Indicate the order of the equation and
what conditions are required for a unique and completely defined
solution to existing. You should solve for the voltage across the
capacitor as the output, y(t), due to the excitation of the input
voltage, x(t), and the initial conditions, y(0) = c0 and
y'(0)=c1.
Compute the homogeneous solution to the ordinary differential
equation for unknown values of R, L...
3. (40 pts total) Eigenvalues of Systems of Equations Application: Series RLC Circuit, Natural, or Transient Response (Remember EE280, maybe not) M SR v(t) Consider a series RLC circuit, with a resistor R, inductor L, and capacitor C in series. The same current i(t) flows through R, L, and C. The switch S1 is initially closed and S2 is initially open allowing the circuit to fully charge. At t=0 the switch S1 opens and S2 closes as shown above. Solving...
use R=1Ω, L=1H and C= 1/5 F Instead
(c) In the circuit shown in Figure P2.61(c), x(t) is the input voltage. The voltage y(t) across the capacitor is considered to be the system output wwww L 1H R=20 + y(t) x(t) C (c) Figure P2.61c (i) Determine the differential equation relating x(t) and y(t) (ii) Show that the homogeneous solution of the differential equation from part (i) has the forme "{K\ej2 + K2e"j2r}, and specify the value of a (iii...
Solve for lapalce transform.
3. For the RLC circuit shown in the graph, determine the current i (t), taking into account that. i(0) = 0 y 9(0) = 0 L = 1 h, R = 1602, C = 10-4f, E = 20v 00000 L E R
Problem 1 (Problem Solving Workshop 1) For a parallel RL circuit R-10, L 1H Determine 1) 21 3) 4) The transfer function H(s) = (s), the pole-zero map, and the step response. Let L(0) - OA The state and output equations. Let Lt) be the state variable The block diagram of this system. Let (O) = -1 The response (t) due to a step input (t) = (t) A) using a known software. Problem #2 (Problem Solving Workshop 1) For...
4. (15 points - PA.3) Consider the RLC circuit shown below, where the input and output x(t) and y(t) are the input voltage vi(t) and capacitor voltage vc(t) respectively, and R = 1 K12, C = 0.1 mF, L = 100 H. i(t) + (i) Determine the frequency response of the system H (jw), as well as its magnitude and phase responses. What type of filter does it correspond to? (ii) Sketch its magnitude and phase response in Matlab. You...
HW 2-1. For the RLC circuit in HW 1-2, with the voltage source x(t) as the 'input' and the loop current y(t) as the 'output' (20 pts) L-11 R=3.22 yo 1) find its frequency response function H(w). (5 pts) 2) then, find its response to the following input signals, respectively 2-a) x(t)=8(t), (2 pts) 2-b) x(t)=u(t), (3 pts) 2-c) x(t)=sin(10t), (3 pts) 2-d) x(t)=2sin(10t)+cos(20t+1), (3 pts) 3) For the signals in 2), calculate the energy or the average power (whichever...
For the circuit shown in Figure 1, determine (a) The transfer function H(s) Vo(s)/V(s) 1 (b). The impulse response h(t) given that R,-5Q, R2-2Q, L,-1 mH, and L2 = 2 mH Ri L R2 Figure 1.
TEE301/05 Question 3 (20 marks) An RLC circuit with a 1V DC source is shown in Fig. 1: i(t) Vout - R-0.22 L-0.1 H C- 10 F Fig. 1 (a) List two properties of Laplace transform. Explain these two properties. [6 marks] (b) Assume that the initial inductor current is OA and initial capacitor voltage is 0.4 V 4 marks] (c) Determine the current, t) in time domain by performing inverse Laplace transform. [4 marks) determine the expression of the...
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