A series RLC circuit has the following component values: R = 20 N, L = 4 H, C = 8 mF, E(t) = 1157 sin t V Determine the type of damping Determine the steady-state current in the circuit
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- Suppose that at any given time t (in seconds) the current i(t) (in amperes) in an alternating current circuit is i(t)=6cost+2sint . What is the peak current for this circuit (largest magnitude)? Leave your answer exact.d) The generated voltage of a turbine at time t seconds is given by: v(t) = Vgsin(0.47at +2) Where Vs is generator voltage in Volts. Evaluate the following: iii. The voltage of the generator after 2.5 seconds if Vs = 70 V. The voltage at time t = 0 seconds to 3 significant figures The time when the generator first reaches maximum voltage, the period, the frequency, and the time displacement. iv. V.c) The charging xoltage in a charging capacitor V(t) at time t seconds is given by: V(t) = V,(1 – e) V Where V, is the supply voltage and t= 60s. Evaluate the following 1. The voltage across the capacitor up to 3 significant figures and in standard form after 36 seconds, if the supply voltage V, = 12 V. The time t in standard form and up to 3 significant figures taken for the 2. capacitor to charge up to 60% of the supply voltage V, which remains at 12 V. 3. Calculate the energy stored in the capacitor when C= 10 mF and t=36 seconds. . E= ½ CV^2). Plot Energy as function of time from 0 to 300 seconds) and show when it 4. reaches the maximum. Explain the result for non-technical audience.
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- In a simple electric circuit, Ohm's law states that V = IR, where V is the voltage in volts, I is the current in amperes, and R is the resistance in ohms. Assume that, as the battery wears out, the voltage decreases at 0.01 volts per second and, as the resistor heats up, the resistance is increasing at 0.03 ohms per second. When the resistance is 300 ohms and the current is 0.04 amperes, at what rate is the current changing? amperes per secondSuppose an RL circuit with a 11 resistor and a 6H inductor is driven by the voltage E(t) est V. If the initial resistor current is I(0) OA, find the current I, the voltages across the inductor E₁ and the resistor ER in terms of time t. A I(t) = = ER(t) EL(t) = = = V VL(cos3t) = S .a s2 +9 s+9 s2 – 9 s2+9 3.
- An RLC circuit with input voltage E(t) is described. Find the current I(t) using the given initial current (in amperes) and charge on the capacitor (in coulombs). 1 R= 84 2, L= 2 H, C = F: E(t) = 196e - 14t tv: (0)= 0, Q(0) = 1 784 I(t) =A 200-volt electromotive force is applied to an RC-series circuit in which the resistance is 1000 ohms and the capacitance is 5 x 102-6 farad. Find the charge q(t) on the capacitor if i (0) = 0.4 A. Determine the charge and current at t= 0.005 s. Determine the charge as %3DQ4. Find the stored energy in a system of four identical point charges, Q = 4nC, at corners of a square 1m on a side. What is the stored energy in the system when only two charges at opposite corners are in place? Ans. 780nJ, 102nJ
