1. The capacitor in the figure is charged with vc (0) = 10 V. Find the mathematical expressions for vc (t) and ix (t) for all time t > 0. 20 μF 2 kn 6 kn t=0,2s 2 k M+10 V +10 Vo VC
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- Fill in all the missing values. Refer to the formulas that follow. Resistance Capacitance Time constant Total time 150 k 100 F 350 k 35 s 350 pF 10 s 0.05 F 1.2 M 0.47 F 12F 0.05 s 86 k 1.5 s 120 k 470 pF 250 nF 100 ms 8 F 150 s 100 k 150 ms 33 k 4 F =RCR=CC=R Totaltime=5Assume that the current flow through the resistor, IR, is 15 A; the current flow through the inductor, IL is 36 A; and the circuit has an apparent power of 10,803 VA. The frequency of the AC voltage is 60 Hz. ET ER EL IT IR15A IL36A Z R XL VA10,803 P VARSL PF LThree 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?
- In this circuit, the capacitance of the capacitor is 1 F, the resistance of the resistor is 1 Ohm, and the battery voltage = 1 V. When the switch is moved from a to b at time t=0, the amount of electric charge stored in the capacitor at t=1 second is approx.. .C.A 60 μF capacitor is connected in series with 40 kΩ resistor across a 120 V supply. Determine (a) the time constant, (b) the current when t = 1.5 mS, (c) the current when t = 5 τ,(d) the voltage at the resistor when t = 1.5 mS, (e) the voltage at the capacitor when t = 1.5 mS, and (f) the time required when VR is equal to VC.Design a single circuit element containing one inductor, one capacitor and one resistor with v(t)=4+2e-3tV and i(t)=2+3e-3tA for t>0. Also specify the value of the inductance, capacitance and the resistance of the three elements.
- The 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 100-pF capacitor is constructed of parallel plates of metal, each having a width W anda length L. The plates are separated by air with a distance d. Assume that L and W are bothmuch larger than d. What is the new capacitance ifa. both L and W are doubled and the other parameters are unchanged?b. the separation d is doubled and the other parameters are unchanged from their initialvalues? c. the air dielectric is replaced with oil having a relative dielectric constant of 25 and theother parameters are unchanged from their initial values ?2. Suppose you want a capacitor bank with a total capacitance of 0.750 F and you possess numerous 1.50 mF capacitors. What is the smallest number you could hook together to achieve your goal, and how would you connect them?
- The circuit shown in the attached image contains a voltage source with emf ε = 2.99 V, a resistor with resistance R = 135 kΩ, and a capacitor with capacitance C = 612 nF. When switch S is set to position a, the three circuit elements are in series. When the switch is in position b, the battery is excluded from the circuit. The switch is initially moved to position a, where it remains for a sufficiently long time that the capacitor is fully charged. The switch is now moved to position b. What is the magnitude of the instantaneous current, in amperes, through the resistor the instant the switch makes contact with terminal b? With time meausred the instant that switch S is closed in position b, calculate the time, in seconds, when the charge on the capacitor is one-half of its maximum value. Calculate the current through the resistor, in amperes, at time t = 155.5 ms after the switch is closed in position b.A 767 uF capacitor has an initial voltage, v(0) = 2 V. If the current flowing through the capacitor is i(t) = 11 mA, what is the voltage v(t) across the capacitor, at time t= 40ms? Enter your answer to 3 significant figures.All capacitors were initially discharged. at t = 0, S1 is placed at position 1 and S2 is closed. Calculate the Thevenin-equivalent voltage seen by the equivalent capacitor during this phase. Enter your answer in V rounded to 2 decimal places. At t = 15 ms, S1 is placed at position 2 and S2 is kept closed. At t = 25 ms, S1 is kept at position 2 and S2 is opened. Data: V1 = 20 V; R1 = 8.0 kΩ, R2 = 10 kΩ, R3 = 2.5 kΩ, R4 = 3 kΩ, R5 = 16 kΩ, R6 = 10.5 kΩ; C1 = 3.5 µF, C2 = 7.0 µF, C3 = 13 µF