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(a) Show that the system of differential equations for the currents iz(t) and iz(t) in the...
(a) Show that the system of differential equations for the currents i2(t) and i3(t) in the...
(a) Show that the system of differential equations for the currents i2(t) and i3(t) in the electrical network shown in the figure below is L1*(di2/dt) + Ri2 + Ri3 = E(t) L2*(di3/dt) + Ri2 + Ri3 = E(t) Solve the system in part (a) if R = 5 Ω, L1 = 0.01 h, L2 = 0.05 h, E = 100 V, i2(0) = 0, and i3(0) = 0. i2(t) = ?? i3(t) = ?? (c) Determine the current i1(t). i1(t)...
The system of differential equations for the currents i1 (t) and i2(t) in the electrical network...
The system of differential equations for the currents i1 (t) and i2(t) in the electrical network shown in the figure is dt(々 =( R2-212/ R2/L1 Use variation of parameters to solve the syster if R1 = 8 Ω, R2-3 Ω, L1 = 1 h, L2-1 h, E(t) = 150 sin(t) V i1(0) = 0, and i2(0) = 0. (i1 (t),ら(t) = R2 し2
A) For the schematic above find the state-space equations that define this system. B) Using the...
A) For the schematic above find the state-space equations that
define this system.
B) Using the controllability rank test determine if this system
is controllable.
C) Using the observability rank test determine if this system is
observable.
1. Controllability and Observability L = 100 m R1 = 10 Ohms Mm R2 = 100 Ohms R4 = 100 Ohms ( = 100 microfarads ult) 1V R3 = 100 Ohms R5 = 100 Ohms Xı = i(t) y = valt) vi(t) =...
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...
1. For the circuit shown in the figure, we wish to find the currents 11, 12,...
1. For the circuit shown in the figure, we wish to find the currents 11, 12, and 13. Use Kirchhoff's rules to obtain equations for a. the upper loop, b. the lower loop, and c. the junction on the left side. In each case, suppress units for clarity and simplify, combining the terms. d. Solve the junction equation for 13. e. Using the equation found in part (d), eliminate 13 from the equation found in part (b). f. Solve the...
1. For the circuit shown in the figure, we wish to find the currents 11, 12,...
1. For the circuit shown in the figure, we wish to find the currents 11, 12, and 13. Use Kirchhoffs rules to obtain equations for a. the upper loop, b. the lower loop, and c. the junction on the left side. In each case, suppress units for clarity and simplify, combining the terms. d. Solve the junction equation for Iz. e. Using the equation found in part (d), eliminate 13 from the equation found in part (b). f. Solve the...
eatu(t), (a >0), is 6(t). Find the response 5. The response of an LTI system to...
eatu(t), (a >0), is 6(t). Find the response 5. The response of an LTI system to e of the system to r(t)= eat cos (Bt)u (t). You have to express the response in terms of 5(t), u (t), sine function, and exponential function. (20 pts) -ly(t)), where * denotes convolution operator. (3) ()[() ]- dt d d Hint: dt
eatu(t), (a >0), is 6(t). Find the response 5. The response of an LTI system to e of the system to...
12 E(t) We see the currents i and i, in the network shown in above, containing...
12 E(t) We see the currents i and i, in the network shown in above, containing an inductor, a resistor, and a capacitor, were governed by the system of First-order DEQ: di dt di dt RC10 Solve the system above under the conditions E(t) 60V, L-1h, R 502, C-10f,and the currents and i are initially zero.
(PHYS 2212K students only) Using the variables in Equations (4), (5) and (6), use Kirchhoff's loo...
see question below:
equations 4,5 & 6:
part D:
my measured values:
(PHYS 2212K students only) Using the variables in Equations (4), (5) and (6), use Kirchhoff's loop rule to algebraically verify that there is only two independent loops in the circuit from Part D. Show the appropriate equation for all the loops and your corresponding calculations. (Use your measured values). Hint: Refer to the Analyzing Circuits with Kirchhoffs Rules" section in the Theory discussion of this experiment. (15 points)...
3-22. An electromechanical system has the following system equations. L. + R1 + Kjw = e(t)...
3-22. An electromechanical system has the following system equations. L. + R1 + Kjw = e(t) - dw J + Bw – K2i = 0 dt T For a unit-step applied voltage e(t) and zero initial conditions, find responses i(t) and wat). Assume the following parameter values: L=1HmJ = kg m², B= 2N ms, R=11, K1 =1V s, K2 = 1 N m/ A.
The system of differential equations for the currents i1 (t) and i2(t) in the electrical network shown in the figure is dt(々 =( R2-212/ R2/L1 Use variation of parameters to solve the syster if R1 = 8 Ω, R2-3 Ω, L1 = 1 h, L2-1 h, E(t) = 150 sin(t) V i1(0) = 0, and i2(0) = 0. (i1 (t),ら(t) = R2 し2
A) For the schematic above find the state-space equations that
define this system.
B) Using the controllability rank test determine if this system
is controllable.
C) Using the observability rank test determine if this system is
observable.
1. Controllability and Observability L = 100 m R1 = 10 Ohms Mm R2 = 100 Ohms R4 = 100 Ohms ( = 100 microfarads ult) 1V R3 = 100 Ohms R5 = 100 Ohms Xı = i(t) y = valt) vi(t) =...
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...
1. For the circuit shown in the figure, we wish to find the currents 11, 12, and 13. Use Kirchhoff's rules to obtain equations for a. the upper loop, b. the lower loop, and c. the junction on the left side. In each case, suppress units for clarity and simplify, combining the terms. d. Solve the junction equation for 13. e. Using the equation found in part (d), eliminate 13 from the equation found in part (b). f. Solve the...
1. For the circuit shown in the figure, we wish to find the currents 11, 12, and 13. Use Kirchhoffs rules to obtain equations for a. the upper loop, b. the lower loop, and c. the junction on the left side. In each case, suppress units for clarity and simplify, combining the terms. d. Solve the junction equation for Iz. e. Using the equation found in part (d), eliminate 13 from the equation found in part (b). f. Solve the...
eatu(t), (a >0), is 6(t). Find the response 5. The response of an LTI system to e of the system to r(t)= eat cos (Bt)u (t). You have to express the response in terms of 5(t), u (t), sine function, and exponential function. (20 pts) -ly(t)), where * denotes convolution operator. (3) ()[() ]- dt d d Hint: dt
eatu(t), (a >0), is 6(t). Find the response 5. The response of an LTI system to e of the system to...
12 E(t) We see the currents i and i, in the network shown in above, containing an inductor, a resistor, and a capacitor, were governed by the system of First-order DEQ: di dt di dt RC10 Solve the system above under the conditions E(t) 60V, L-1h, R 502, C-10f,and the currents and i are initially zero.
see question below:
equations 4,5 & 6:
part D:
my measured values:
(PHYS 2212K students only) Using the variables in Equations (4), (5) and (6), use Kirchhoff's loop rule to algebraically verify that there is only two independent loops in the circuit from Part D. Show the appropriate equation for all the loops and your corresponding calculations. (Use your measured values). Hint: Refer to the Analyzing Circuits with Kirchhoffs Rules" section in the Theory discussion of this experiment. (15 points)...
3-22. An electromechanical system has the following system equations. L. + R1 + Kjw = e(t) - dw J + Bw – K2i = 0 dt T For a unit-step applied voltage e(t) and zero initial conditions, find responses i(t) and wat). Assume the following parameter values: L=1HmJ = kg m², B= 2N ms, R=11, K1 =1V s, K2 = 1 N m/ A.
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