Capacitors in Figure Ql(a) has been charged up to its steady state condition. For each of the capacitors, C, and Cz: (a) (i) Find the voltage, Vị and V3. (ii) Find the charge, Qi and Q2. (ii) Calculate the energy in each capacitor. + V, - C; = 2 µF + V2 - C=3 µF he 20 2 V Figure QI(a)
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- Three capacitors having capacitance values of 20F,40F, and 50F are connected in parallel to a 60 - Hz power line. An ammeter indicates a circuit current of 8.6 amperes. How much current is flowing through the 40F capacitor?You are an electrician working in an industrial plant. You discover that the problem with a certain machine is a defective capacitor. The capacitor is connected to a 240-volt AC circuit. The information on the capacitor reveals that it has a capacitance value of 10 mF and a voltage rating of 240 VAC. The only 10-mF AC capacitor in the storeroom is marked with a voltage rating of 350 WVDC. Can this capacitor be used to replace the defective capacitor? Explain your answer.Switch S in in the figure is closed at time t = 0, to begin charging an initially uncharged capacitor of capacitance C = 16.1 μF through a resistor of resistance R = 20.7 Ω. At what time is the potential across the capacitor equal to that across the resistor?
- Suppose that at t=0, we connect an uncharged 10{μF capacitor to a charging circuitconsisting of a 2500-V voltage source in series with a 2{MΩ resistance. At t=40s, the capacitoris disconnected from the charging circuit and connected in parallel with a 5{MΩ resistor.Determine the voltage across the capacitor at t=40 s and at t=100 s. (Hint: You may find itconvenient to redefine the time variable to be t′=t−40 for the discharge interval so that thedischarge starts at t′=0.)You measure the capacitanceC1of a capacitor by doing thefollowing: First connect capacitorsC1andC2in series to a power sup-ply that provides a voltageVthat can be varied. The capacitance ofC2is known to be3.00mF. Then vary the applied voltageV, and for eachvalue ofVmeasure the voltageV2acrossC2. After plotting your data asV2versusV, you find that the data fall close to a straight line that hasslope 0.650. What is the capacitanceC1?A small capacitor of 100 pF is charged by a steady current of 1 µA for 1 ms. At that time, the charging circuit is disconnected. a) What is the voltage across the capacitor when the charging finishes? b) A 10 MΩ resistor is connected across the capacitor to discharge it. Sketch a graph of the voltage V across the resistor as a function of time, with appropriate numbers and units marked on the axes.
- A series circuit consisting of an inductor, a resistor, and a capacitoris open. There is an initial charge of 2 coulombs on the capacitor,and 3 amperes of current is present in the circuit at the instantthe circuit is closed. A voltage given by E(t) = 20 cos t is applied.In this circuit the voltage drops are numerically equal to thefollowing: across the resistor to 4 times the instantaneous changein the charge, across the capacitor to 10 times the charge, andacross the inductor to 2 times the instantaneous change in the current.Find the charge on the capacitor as a function of time. Determinethe charge on the capacitor and the current at time t = 10.For 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. ..For the circuit in the figure, initially the switch S is closed in (b), until the capacitor is charged; then the switch goes to point (a) so that the battery is disconnected and the capacitor, resistor and inductor are connected in series. Once S is connected at point (a), find a) the angular frequency of oscillation for the series circuit b) write the equation for the charge on the capacitor as a function of time with the respective values of Qmax, angular frequency Wd and time T c) make the Q(t) graph showing explicitly the envelope of the exponential decay (Hint: use geogebra or an application of your choice to obtain a graph).
- 1. Inquire about the operational and geometric definitions of capacitance C. [C = = ε0 , please refer to previous lesson on capacitance.] 2. Have the students write down the meaning of each of the symbols present in the above definitions.Suppose that we have two 100-μF capacitors. One is charged to an initial voltage of 50 V, and the other is charged to 100 V. If they are placed in series with the positive terminal of the first connected to the negative terminal of the second, determine the equivalent capacitance and its initial voltage. Now compute the total energy stored in the two capacitors. Compute the energy stored in the equivalent capacitance. Why is it less than the total energy stored in the original capacitors?Two initially uncharged capacitors C 1 = 15 μF and C 2 =10 μF are connected in series. Then, a 10-V source is connected to the series combination, as shown in Figure P3.28. Find the voltages v1 and v2 after the source is applied. [Hint: The charges stored on the two capacitors must be equal, because the current is the same for both capacitors.]