The energy that is stored in a 30-μF capacitor is w(t) = 12 sin2100. Find the current in the capacitor.
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- Assume that the voltage drop across the resistor, ER, is 78 V, that the voltage drop across the inductor, EL, is 104 V, and the circuit has a total impedance, Z, of 20 . The frequency of the AC voltage is 60 Hz. ETITZ20VAPFER78VIRRPEL104VILXLVARsLLThe current in the capacitor is 0 for t<0 and 3 cos 50,000t A for t≥0. Find (a) v(t); (b) the maximum power delivered to the capacitor at any one instant of time; and (c) the maximum energy stored in the capacitor at any one instant of time.A series circuit has a capacitor of 1.5625x10^(-8)F a resistor of 2x10^4 ohms, and an inductor of 1H. If the initial charge on the capacitor is zero,. if a 12-volt battery is connected to the circuit and the circuit is closed at t=0, determine the charge on the capacitor at any time t
- The current in a 20 mH inductor is known to be i=40 mA,t≤0; i=A1e−10,000t+A2e−40.000tA,t≥0. The voltage across the inductor (passive sign convention) is 28 V at t=0. 1. Find the expression for the voltage across the inductor for t>0. 2. Find the time, greater than zero, when the power at the terminals of the inductor is zero.For the circuit shown, calculate 1. the initial energy stored in the capacitors; 2. the final energy stored in the capacitors; 3. the total energy delivered to the black box; 4. the percentage of the initial energy stored that is delivered to the black box; and 5. the time, in milliseconds, it takes to deliver 7.5 mJ to the black box.A 20μF capacitor is subjected to a voltage pulse having a duration of 1 s. The pulse is described by the following equations: vc(t)={30t2 V,0≤t≤0.5 s;30(t−1)2 V,0.5 s≤t≤1 s;0elsewhere. Sketch the current pulse that exists in the capacitor during the 1 s interval.
- An uncharged 0.2 μF capacitor is driven by a triangular current pulse. The current pulse is described by i(t)={0,t≤0;5000t A,0≤t≤20 μs;0.2−5000t A,20≤t≤40 μs;0,t≥40 μs. Derive the expressions for the capacitor voltage, power, and energy for each of the four time intervals needed to describe the current.For t < 0, the capacitor in the given figure is completely discharged. Assume that the switch is thrown at t = 0. Let VS = 15 V, R = 200 Ω, L = 20 mH, and C = 0.1 μF.A parallel plate capacitor has plates 20 mm apart, a plate area of 120 sq.cm. and a dielectric with relative permittivity of 2. Determine the capacitance if the capacitor has a charge of 0.06 μC. Express in nano-farad, five decimal places.
- An electrical circuit has a very small resistance so it can be despised. The capacitor on the left was charged up to the voltage of Vo=10 volts and then, at time t=0, the switch S was closed. The capacity of the capacitors are C=60 µF, and the coil inductance is L=0.04 HI) Find the voltage on the left capacitor, at the instant V1=0.001 s.II) Find the voltage in the right capacitor, at the instant t=002 s.6 A capacitor is constructed with parallel metal plates, If the plate separation is 2 mm and the capacitance is given to 1 nano Farads, determine the area of the parallel plates of the device. Select one: a. 0.12 square meters b. 0.23 square meters c. 0.27 square meters d. 0.20 square metersThe current at the terminals of the two capacitors shown is 240e −10tμA for t≥0. The initial values of v1 and v2 are −10 V and −5 V, respectively. Calculate the total energy trapped in the capacitors as t→∞. (Hint: Don’t combine the capacitors in series—find the energy trapped in each, and then add.)