P3.1 An RLC circuit is shown in Figure P3.1. (a) Identify a suitable set of state variables. (b) Obtain the set of first-order differential equations in terms of the state variables. (c) Write the state differential equation Figure P3.1 RLC circuit v(t) Voltage source - R i(t) L vc(1)
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Problem 3.1 (Rename R to R1 and add R2 in parallel with C.)
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- Write down the Kirchhoff Junction equation and solve it for I, in terms of I, and I3. Write the result here: I1 Write down the Kirchhoff Loop equation for a loop that starts at the lower left corner and follows the perimeter of the circuit diagram clockwise. 0 = Write down the Kirchhoff Loop equation for a loop that starts at the lower left corner and touches the components 4V, R2, and R3. 0 = The resistors in the circuit have the following values: R1 = 13 N R2 = 6 N R3 = 2 N Solve for all the following (some answers may be negative): I1 Amperes I, = Amperes I3 = Amperes NOTE: For the equations, put in resistances and currents SYMBOLICALLY using variables like R1,R2,R3 and I,I2,I3. Use numerical values of 10 and 4 for the voltages.S 3. For the circuit shown to the right, the resistance is 4,000 Ohms, the capacitance is 100x10-6 F, and the battery is 30 V. + C a. What is the time constant for the circuit?. b. What is the current in the circuit at t = 0 and t = infinity? c. What is the current in the circuit as a function of time?Problem 3: Show how to calculate the noise figure (NF2) for a particular circuit fed from a source with internal resistance Rs2 knowing its noise figure (NF1) when it is fed from a source with internal resistance Rs1. In your solution sketch the system as usual.
- Give the symbolic expression for the emf E using KVL for the circuit with S1 closed and S2 open. Give your answer in terms of the current I, resistor R, capacitors C1 and C2 and charges stored in the respective capacitors Q1 and Q2. Use * to denote product and / to denote division. So to group the product of, say, a and b_1 write a*b_1. And to write a ratio of say, c_1 and d write c_1/d. To add the product and ratio write a*b_1 + c_1/d . a)Write the mathematical expression for emf E. E= In the figure there's a circuit with an emf E=21V, two resistors R1=35kΩ and R2=5.5kΩ, two capacitors C1=25μF and C2=22μF and two switches S1 and S2. b) Find the time constant for this configuration of the circuit. Time constant τ c) Find how much charge will be stored in C2 after time t=1.3τ seconds. Charge stored in C2 PartII After t=10τ seconds, we open switch S1 and close switch S2. Mark current time as t′=0. In this configuration, capacitor C2 discharges through the resistor R2. d) Find…A large capacitor of 3000 µF is charged by a constant current. After 1 minute it reaches a voltage of 100 V. At that voltage, the charging circuit is disconnected. a) Calculate the charging current. b) A second identical capacitor is connected across the capacitor, using wires with 1 kN re- sistance. Sketch a graph of the voltages on the two capacitors as a function of time, with appropriate numbers and units marked on the axes.Question 2 -12 Use the following constants if necessary. Coulomb constant, k = 8.987 x 10° N m2 /C2. Vacuum permitivity, €o = 8.854 x 10 Permeability of vacuum, µo electron, me = 9.10938356 x 10 31 kg. Unless specified otherwise, each symbol carries their usual meaning. For example, µC means micro coulomb F/m. Magnetic 12.566370614356 × 10 H/m. Magnitude of the Charge of one electron, e = -1.60217662 x 10-19 C. Mass of one Ri Rz P E3 Ry ww Ra
- 1. 2. 3. Identify whether the circuit is connected in series or in parallel. a. a. 12V a. C1 Is + Ri C2 VI₂ M C3 R3 5 VI b. b. MMM R₂ Ri b. + C1 VCI ㅣ사 R3 C2 VC₂ VCxy C3 VC3For R1=20, R2=50, R3=20, R4=10, R5=10, V1=25 V, V2=35 V & 11=6 A in the circuit shown below, apply source transformation to find Vx (in volt) RI R3 RS V1 R2 R4 v2Problem 3: Consider a circuit shown in the figure. Ignore the internal resistances of the batteries. ℰ1 = 34 Vℰ2 = 46 VR1 = 10 ΩR2 = 4 ΩR3 = 8 Ω. 1. Write the equation of potential change in loop DCAF in terms of the circuit elements. 2. Solve the three equations to get I3. 3. Calculate the numerical value of I3 in A. 4. Calculate the numerical value of I2 in A. 5. Calculate the numerical value of I1 in A.
- Problem 2: For the circuit show below, what are I₁, I2,I3? ε₁ = 8V, ε₂ = 12V, R₁ = 6 N, R₂ = 2, R3 = 4 N. Answers: 1₁ = 1.64 A, I₂ = 0.91 A, I3 = 2.55 A. https://www.handymath.com/cgi-bin/matrix3d.cgi R3 E2 13 13 R2 12 12 R₁ 11 Γω I₁ELECTRICAL POTENTIAL AND CURRENT: V IR E-P P IV C Pt Series Circuits: Parallel Circuits: V, = V, + V,+ V, +. V, = V, = V, V, .. 1. 1. R, = R, + R, + R, +. RT R, R Based on the circuit drawn below: (Please use your VIRP chart) R = 15 Q V = 120 V R2 = 20 2 R3 5 2 W-To measure signal propagation in a nerve in the arm, the nerve is triggered near the armpit. The peak of the action potential is measured at the elbow and then, 4.0 ms later, 24 cm away from the elbow at the wrist.a. What is the speed of propagation along this nerve?b. A determination of the speed made by measuring the time between the application of a stimulus at the armpit and the peak of an action potential at the elbow or the wrist would be inaccurate. Explain the problem with this approach, and why the noted technique is preferable.