1. For a circuit with the following given: E = 50V, R = 10 ohms and C = 4(10)-4 farad. Assume that when the switch is closed (at t = 0), the charge on the capacitor is 0.015 coulomb. Find the initial current in the circuit and the current at t > 0.
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- (a) Determine the equilibrium charge on the capacitor in the circuit shown as a function of R. (b) Evaluate the charge when R = 10.0 Ω. (c) Can the charge on the capacitor be zero? If so, for what value of R? (d) What is the maximum possible magnitude of the charge on the capacitor? For what value of R is it achieved? (e) Is it experimentally meaningful to take R = ∞? Explain your answer. If so, what charge magnitude does it imply?2. A parallel plate capacitor with a plate area of 0.13 square meters separated by 1 mm is charged to 9 Volts by a battery, which is then disconnected. The plate separation is then increased to 40 mm.A. Using the expression for the capacitance of a parallel plate capacitor, what do you expect the new potential difference across the plates to be after the increase?B. Suppose you measure the potential difference across the plates after the separation and find it to be 30 V (this should be very different from what you found in part A). This unexpected result can be explained by the effects of “stray capacitance” with nearby objects. Assuming that the stray capacitance can be modeled as a capacitor connected in parallel with the parallel plate capacitor, find the value of this stray capacitance.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 SECONDS
- A potential difference V(t) = V0sin ωt ismaintained across a parallel-plate capacitor withcapacitance C consisting of two circular parallel plates. Athin wire with resistance R connects the centers of the twoplates, allowing charge to leak between plates while theyare charging.(a) Obtain expressions for the leakage current Ires(t) in thethin wire. Use these results to obtain an expression for thecurrent Ireal(t) in the wires connected to the capacitor.(b) Find the displacement current in the space between theplates from the changing electric field between the plates.(c) Compare Ireal(t) with the sum of the displacementChapter 16 | Electromagnetic Waves 733current Id(t) and resistor current Ires(t) between theplates, and explain why the relationship you observe wouldbe expected.A 3.0 MΩ resistor and a 1.0 μF capacitor are connected in series with an ideal battery that has an emf E = 5.0 V. After 1.0 s after the initial connection is made, find the rate at which(a) the charge on the capacitor is increasing (inC/s),(b) energy is being stored in the capacitor (inJ/s),(c) thermal energy is appearing in the resistor (inJ/s), and (d) energy is being delivered by the battery (inJ/s).Derive an expression for the electrical energy stored in a capacitor of capacitance C when charged to a potential difference V. If C = 2µF and V= 4V, calculate(l.) the final energy stored in the capacitor,(II.) the work done by the battery in the charging process Account for any difference between your answers in parts (I) and (II) above
- Let the first order circuit be shown in the following figure:The switch shown is known to change itsstate from open to closed at time t = 0 and that,once this change has occurred, the circuit reaches thesteady state at approximately 4.5 μs.a) Find the expression for the voltage v (t), for all t> 0, and graph, soapproximate, its behavior as a function of time.b) Find the value of the inductance L.Given the circuit below with the switch closed for a long time, then opening at t=0, and with the values R1=129KΩ, R2=128KΩ, R3=103KΩ, calculate the time constant, τ, for the capacitor voltage solution for at t >0.Consider the circuit below. a) Calculate the equivalent capacitance Ceq (show all steps) b) What is the potential difference across C4?
- A circuit consists of switches that open or close at t=0, resistances, dc sources, and a single energy storage element, either an inductance or a capacitance. We wish to solve for a current or a voltage x(t) as a function of time for t≥0. Write the general form for the solution. How is each unknown in the solution determined?decide if the given statement is true or false,and give a brief justification for your answer.If true, you can quote a relevant definition or theorem . If false,provide an example,illustration,or brief explanation of why the statement is false.Q. If there is no driving electromotive force in an RLC circuit,then the charge on the capacitor and the current in the circuit tend to zero as t →∞The figure shows an electrical circuit with an ideal source ε1 = 12 [V], a real source ε2 = 9 [V] and r1 = 1 [Ω], eight resistors and two capacitors. Switches A and B areThey are originally open and the charge on the capacitors is zero. If at t = 0 [s] switch A opens and switch B closes, determine:d) The potential difference of resistor R8 at t = 2.6 [s].e) The time required for the potential difference of the equivalent capacitor to reach the maximum possible value. Justify your answer.