Q47 In the circuit shown below, the initial capacitor voltage is 4 V. Switch S1 is closed at t=0. The charge (in µC) lost by the capacitor form t= 25 µs to t= 100 µs is
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- 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).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.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…
- 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 SECONDSDerive 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. If a 4μF capacitor is connected to a constant current source, therefore its current is given in the equation ic(t)=10mA. Determine the voltage, power and energy at 2ms.
- 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).Prior to t=0, the current in a 2-H inductance is zero. Starting at t=0, the current is increased linearly with time to 10 A in 5 s. Then, the current remains constant at 10 A. Sketch the voltage, current, power, and stored energy to scale versus time.Consider a coaxial capacitor, radius a and b, and length L, as shown in the figure below.The capacitor it is partially filled with dielectric (ɛ, length D).The rest is air (ɛ0). Consider that (L, D >> (b-a)). The inner conductor (r = a) is held at constant potential V and the outer conductor (r = b) is grounded.I)Determine capacitanceIl)Consider the situations D → 0 and D → L. Determine the new capacitance values
- 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…Given an initially charged capacitance that begins to discharge through a resistance at t=0, what percentage of the initial voltage remains at two time constants? What percentage of the initial stored energy remains?The voltage across an inductance L is given by v( t )= V m cos( ωt ). The current is zero at t=0 .Suppose that is very large ideally, approaching infinity. For this voltage, does the inductance approximate either an open or a short circuit? Explain.