(!) THE FOLLOWING QUESTIONS ARE BASED ON THE INFORMATION GIVEN HERE. R2 ww The emf source, E = 2.1 V, of the circuit shown in the figure has negligible internal resistance. The resistors have resistances R, = 2.6 N and R2 = 5.6 2. The capacitor has a capacitance C = 3.7 µF. R1 A) Determine the time constant T, in units of microseconds, for charging the capacitor. Answer: B) What is the charge Q on the capacitor in units of microcoulomb? Answer:
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- The triangular current pulse shown in the provided figure is applied to a 500 mH inductor. 1. Use passive sign convention. Derive the expression for the inductor energy in Joules at the interval 0 ≤ t ≤ 25 ms in the form w = At^2 + Bt + C Joules, where ^2 refers to "to the power of 2". Provide the value of A in the equation. 2. Derive the expression for the inductor energy in Joules at the interval 25 ms ≤ t ≤ 50 ms in the form w = At^2 + Bt + C Joules, where ^2 refers to "to the power of 2". Provide the value of B in the equation. 3.2. 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.The triangular current pulse shown in the provided figure is applied to a 500 mH inductor. A.) Use passive sign convention. Calculate the inductor energy in Joules at the interval t < 0. B.) Derive the expression for the inductor energy in Joules at the interval 0 ≤ t ≤ 25 ms in the form w = At^2 + Bt + C Joules, where ^2 refers to "to the power of 2". Provide the value of A in the equation. C.) Derive the expression for the inductor energy in Joules at the interval 25 ms ≤ t ≤ 50 ms in the form w = At^2 + Bt + C Joules, where ^2 refers to "to the power of 2". Provide the value of B in the equation. D.)
- 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 SECONDSGiven 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.In the circuit diagram below, the capacitor C is first fully charged by using a 6.0V battery and the two way switch k. It is then discharged through the resistor R. The figure below shows how the charge Q on the capacitor C changes with time during the discharge. Use the graph to answer the following questions: What is the capacitance of the capacitor? Estimate the initial current through the resistor during the discharging process, hence, calculate the resistance of the resistor and the time constant of the circuit. On the same axes, draw graphs to show how the voltage Vc across the capacitor and VR across the resistor vary with time during the charging. Indicate values where appropriate.
- (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?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)Just after the switch is closed, what is the magnitude of the potential difference Vab across the resistor R1? B)Magnitude of the potential difference Vcd across the inductor L? C)The switch is left closed a long time then opened. Just after the switch is opened, what is the magnitude of the potential difference Vab across the resistor R1? D)What is the magnitude of the potential difference Vcd across the inductor L?
- 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) aboveFor the circuit shown in the figure, in which the capacitor is initially fully discharged. If the source voltage V is 17 Volts, the capacitance of capacitor C is 24 mF; and the values of the resistors in Ω are: R1 = 2250 , R2 = 1071 , R3 = 2455 , R4 = 1199 and R5 = 1043 Determine the voltage across the capacitor in Volts after 15 minutes have elapsed since the circuit is energized. ..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 (b) Now take an imaginary flat disc of radius r < a inside the capacitor, as shown below. 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…