Suppose you have the following circuit. The switch has been open for a long time, and is closed at time t = 0. Assume V₂ = 5V, R₂ = 10kN, L2 10kn, L2 = 2mH, C₂ = 0.1μF The second order differential equation for the voltage across the capacitor is d²Vc(t)/dt + a₁dVc(t)/dt + a₂Vc = K
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- Can you please help with this question? The triangular voltage pulse shown below is applied to a 200 mF capacitor. a) Write the expressions thatdescribe vc(t) in the five time intervals t < 0, 0 ≤ t ≤ 2 , 2 ≤ t ≤ 6, 6 ≤ t ≤ 8, and t > 8. b) Derive theexpressions for the capacitor current, power, and energy for the time intervals in part (a).Consider the circuit below with V = 40 V, R1 = 12 ohms, R2 = 18 ohms, R3 = 30 ohms, and C1 = 60 mF. The switch in the circuit has been closed for a long time before it is opened at t = 0. 1:Find the initial voltage across the capacitor. 2:For the natural response of the circuit after t > 0, find the time constant for the circuit. 3:Find the expression for the magnitude of the voltage across the capacitor. 4:Find the expression for the magnitude of the current through R3.The circuit elements in the circuit L=50 mH, and C=0.2 μF. The initial inductor current is−45 mA and the initial capacitor voltage is 15 V. The resistance is increased to250 Ω. Find the expression for v(t) for t≥0.
- Given the circuit below with the switch closed for a long time, then opening at t=0, and with the values R1=193KΩ, R2=186KΩ, R3=107KΩ, calculate the capacitor voltage at t =0.Please answer ASAP and I'll upvote, thank you. In the given circuit, switch S1 is in position A and 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 S2remains open. 10ms after switch S1 moves to position B, switch S2 is closed and remains closed for 20ms only. Determine the expressions for the inductor current for 0≤t<10ms, 10ms≤t<30ms, 30ms≤t<∞, and determine 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 uncharged capacitor in the circuit is initially switchedto terminal a of the three-position switch. At t=0, the switch is moved toposition b, where it remains for 15 ms. After the 15 ms delay, the switch ismoved to position c, where it remains indefinitely. 1. Derive the numerical expression for the voltage across the capacitor.
- Now suppose the switch in the circuit in has been inposition b for a long time. At t=0, the switch moves instantaneouslyto position a and stays there. Find the initial and final values of thecapacitor voltage, the time constant for t≥0, and the expression forthe capacitor voltage for t≥0An RC circuit with a capacitance of 1E-1 farad, and a resistance of 2Ω, has an EMF of E(t)=4cos(t) volts applied to it. a. Find the charge on the capacitor, q(t), with q(0)=6/13, and the subsequenct current, I(t). Solve the problem mathamatically (DE) and try to restrain yourself from solving it using your physics knowledge.The circuit shown is at steady state before the switch closes. The inductor currents are both zero before the switch closes (i1(0) = i2(0) = 0). The voltage across the 2H-inductor is 4e-5t V for t > 0, otherwise 0V for t < 0. (a) Determine the inductor currents i1(t) and i2(t) for t ≥ 0. (b) Determine the energy stored by each inductor 200ms after the switch closes. (c) In the equivalent inductor (for the parallel inductors) determine the (i) current and the (ii) energy stored for 200 ms after the switch closes. Answer: 0.4(1 − e−5t) A, 0.1(1 − e−5t) A, 16.0mJ, 63.9mJ, 316mA, 79.9mJ
- 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 voltagesource by a thin wire. A switch in the circuit is closed at time t = 0 and a current I(t) flows in the circuit. Thecharge on the plate is related to the current according to I (t) = dq/dt. We begin bycalculating the electric field between the plates. Throughout this problem you mayignore 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 functionof 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, as shownbelow. Using your expression for E above, calculate the electric flux through this flatdisc 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…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 triangular voltage pulse shown below is applied to a 200 mF capacitor. a) Write the expressions thatdescribe vc(t) in the five time intervals t < 0, 0 ≤ t ≤ 2 , 2 ≤ t ≤ 6, 6 ≤ t ≤ 8, and t > 8. b) Derive theexpressions for the capacitor current, power, and energy for the time intervals in part (a).