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ELECTRICAL ENGINEERING(LL)-W/MODMAS AC
- A resistor (5 Ω) and capacitor (0.05 F) are joined in series with an electromotive force E(t) = 30 −t V. If there is nocharge on the capacitor at time t = 0, find the ensuing charge on the capacitor at time t. The following lineardifferential equation models the charge on the capacitor, q(t). (check the image) How do I go about solving this?arrow_forwarda. Find the mathematical expressions for the transient behavior of thevoltage vC and the current iC if the capacitor was initially unchargedand the switch is thrown into position 1 at t = 0 s.b. Find the mathematical expressions for the voltage vC and the current iCif the switch is moved to position 2 at t = 3 ms.c. Find the mathematical expressions for the voltage vC and the current if theswitch is thrown into position 3 at t =5 ms.d. Plot the waveforms obtained in parts (a)–(c)arrow_forwardFor 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).arrow_forward
- 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?arrow_forwardIn the figure given below, the capacitor is initially uncharged. Suppose C = 500µF.At t = 0 s, the switch is moved to position 1 for 5 ms, then to position 2 and it remains there. DeterminevC and iC while the switch is in position 2.arrow_forwardThe capacitor is discharged through a resistor with the resistance R = 10000 Ohm with a relaxation time of 10 ms. What is the capacitance of the capacitor? What is the charge of the capacitor after time 25 ms after the beginning of discharging if the initial charge was 20 nC?arrow_forward
- Assume at t=0, a switch in an RC circuit in which the resistor and capacitor are in parallel is closed. how would this affect voltage, charge, and current at t=0 and after a very long time? what if this scenario was the opposite, in which the switch was opened rather than closed? what effect would this have?arrow_forwardFor the circuit below, R1 is given by the "6". The value of capacitorC1= 15 µF. a-) find ?0(?) for ? > 0. Deteremine the time constant and find the time necessary for the capacitor voltage to decay to one-tenth of its value at t = 0. Sketch the voltage on the capacitor.b-)Add another capacitor with same value in parallel. What will be the total capacitance. Find the time constant. Which parameters will be affected by the addition of the capacitor? Explain. Draw the input and output waveformsarrow_forwardThe current through a 100-mH inductance is given by i( t )=exp( −t ) sin( 10t ) in which the angle is in radians. Determine the voltage across the inductance. Then, use the computer program of your choice to plot both the current and the voltage for 0≤t≤3 s.arrow_forward
- Q1 b) Derive the current waveform for a 10μF capacitor if the voltage across the capacitor is as shown in Figure Q1(b). c) The voltage across a 10 F capacitor is v(t) = 5te-2t V. Determine the current that flows into the capacitor and the electrical power of the capacitor. d) Calculate the voltage across each capacitors in Figure Q1(d) during steady state.arrow_forwardAn unusual capacitor has a capacitance that is a function of time given by C=2+cos( 2000t ) μF in which the argument of the cosine function is in radians. A constant voltage of 50 V is applied to this capacitor. Determine the current as a function of time.arrow_forwardV(t) = V0e^-t/rc where V(t) is the voltage across the capacitor after it's been discharging for an amount of time t, V0 is the voltage it started at, C is the capacitance of the capacitor, and R is the resistance of the resistor it's discharging through. One thing we can take away from this is that, after it's been discharging for an amount of time t = RC, the voltage across the capacitor will be V0e^−1, which is about 37% of the voltage it started at. In other words, RC, the resistance times the capacitance, is the amount of time it takes the capacitor to discharge from 100% voltage to 37% voltage. (The units check out, by the way: 1Ω⋅1F=1sec) If you have an RC circuit with a 10 mF capacitor and a 2 kΩ resistor, about how long will it take the capacitor to discharge to 37% of its original voltage? Group of answer choices 100 s 5 s 12 s 20 sarrow_forward
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