The inductors in the circuit shown are initially charged and are connected to the Black Box at time t= 0. If iz(0) = 4 A, iz(0) = -3 A and v(t) = 50 e- 200t mV for t 2 0, find: a) The initial energy stored in each inductor b) iz(t) = ? for t 2 0, c) iz(t) = ? for t > 0 %3D
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- An inductance of 1 H, a resistance of 8 Ω and capacitance of 0.04 F are connected in series with a variable voltage E = 50 sin 3t. Find the current and charge in the system, given the initial conditions q = 0 and l = 0 when t = 0, using method of solution of higher order linear ordinary differential equation.All capacitors were initially discharged. at t = 0, S1 is placed at position 1 and S2 is closed. During this phase, it has been determined that Eth and Rth seen by the equivalent capacitor are, respectively, 20 V and 6.0 kΩ. The time constant is 29 ms. At t = 15 ms, S1 is placed at position 2 and S2 is kept closed. Calculate the equivalent capacitor voltage vT at t = 15 ms. Enter your answer in V rounded to 2 decimal places. At t = 25 ms, S1 is kept at position 2 and S2 is opened. Data: R1 = 5 kΩ, R2 = 3 kΩ, R4 = 2 kΩ, R5 = 20 kΩ, R6 = 12.0 kΩ;The voltage pulse applied to the 100 mH inductor shown is 0 for t<0 and is given by the expressionv(t)=20te−10t V for t>0. Also assume i=0 for t≤0.. Find the inductor current as a function of time.
- From the given circuit. Switch S1 is in position A switch S2 is open. Both switches are in these states for a very long time. At t=0, switch S1 moves from position A to B while switch S2 remains open. 10ms after switch S1 moves to position B, switch S2 is closed and remains closed for 20ms only. ANSWER THE FOLLOWING: a.) Expression for the inductor current for 0 ≤ ? < 10??b.) Expression for the inductor current for 10?? ≤ ? < 30?? and 30?? ≤ ? < ∞c.) What is the time (in ms) after switch S1 moves to position B is the current in the inductor equivalent to 30% of the initial value (at ?=0).The equation for the voltage ?(?) across a capacitor at time ? is?(?)=1?(∫?(?)???0+?0)Where ?(?) is the current passing through the capacitor, and ?0 is the initial charge. Consider a capacitor with ?=1?? and ?0=0. If ?(?)=0.1(0.2+sin0.5?) A, find ?(?) for ?=0.5 sec.Consider the given circuit. The switch has been closed for a very long time before opening at t=0s. Determine the capacitor voltage (in volts) right before the switch has been opened, the time constant of the circuit for t>0 (in ms), and the expression for the capacitor voltage for t≥0.
- The current flowing through a 10-μF capacitor having terminals labeled a and b is i ab =0.3 exp( −2000t ) Afor t≥0 Given that v ab ( 0 )=0, find an expression for v ab (t) for t≥0. Then,find the energy stored in the capacitor for t=∞..The circuit shown below is an underdamped system, and the current through the inductor has the form iL(t)=e^at ( ) (K1sinwt + K2coswt ) for t≥0 a. Determine the numerical values, including signs, of a and w b. If the initial conditions are iL(0) = 1A and Vc (0) =12V , determine the numerical values, including signs, of K1 and K2 c. Using the numbers determined above, write out the complete expression for iL(t)Consider the circuit above. The switch has been closed for a very long time before opening at t=0s. Determine the Inductor current (in amperes) right after the switch has been opened, the time constant of the circuit for ?>0 (in ms), and the Expression for the inductor current for ?≥0.
- IN THE CIRCUIT SHOWN, CONSIDER THAT V1=20 VDC, R1=1000 Ω, R2=3000 Ω, R3=3500 Ω AND C=1 mF.DETERMINE:A) THE TIME IT TAKES FOR THE CAPACITOR TO REACH ITS FINAL VALUE (5T), WHEN SWITCH 2 (INT 2) IS IN POSITION A AND SWITCH 1 (INT 1) IS CLOSED AT t=0,B) THE ENERGY STORED BY THE CAPACITOR ONCE IT HAS BEEN FULLY CHARGED WITH THE SAME POSITION OF SWITCHES AS ITEM A)C) ONCE THE CAPACITOR HAS BEEN FULLY CHARGED WITH SWITCH 1 CLOSED, SWITCH 2 MOVES POSITION (GOES TO B) AT A NEW t=0. NOW DETERMINE THE VALUE OF THE VOLTAGE ON THE CAPACITOR AT t=3.5 SECONDSThe voltage pulse applied to the 100 mH inductor shown is 0 for t<0. and is given by the expression v(t)=20te−10t V for t>0. Also assume i=0 for t≤0. Sketch the voltage as a function of time.1. A capacitor consists of two circular plates of radius a separated by a distance d (assume d << a). The centre of each plate is connected to the terminals of a voltage source by a thin wire. A switch in the circuit is closed at time t = 0 and a current I(t) flows in the circuit. The charge on the plate is related to the current according to I (t) = dq/dt. We begin by calculating the electric field between the plates. Throughout this problem you may ignore edge effects. We assume that the electric field is zero for r > a. (A) Use Gauss’ Law to find the electric field between the plates as a function of time t, in terms of q(t), a, ε, and π. The vertical direction is the k direction. (B) Now take an imaginary flat disc of radius r < a inside the capacitor, Using your expression for E above, calculate the electric flux through this flat disc of radius r < a in the plane midway between the plates, in terms of r, q(t), a, and ε. (C) Calculate the Maxwell displacement…