2. The equation of electric charge on the capacitor is related to the equation of currentstrength with the equation i=dq/dt. So, the equation forms a second-order differentiald²qdq1Ldt+ R,+79 = E(t)dtequation. Determine the special charge equation with the equation q(t) on the capacitor inthe RLC circuit when the value of L= 0.25 Henry,R=10 ohms,C=0.001 Farads,E(t)=0,q(0)=q0coulombs(C) and i(0)=0 Ampere.

Given the differential equation in RLC circuit as : Ld2qdt2+Rdqdt+1Cq=E(t) Given: R=10 Ω, L=0.25 H,…

Answered: 2. The equation of electric charge on…

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.27P

See similar textbooks

Similar questions

Application of Differential Equation A circuit has in series of electromotive force given by E(t) = 100 sin 60t V, a resistor of 2 Ω, an inductor of 0.1 H, and a capacitor of 1/260 farads. If the initial current and the initial charge on the capacitor are both zero coulombs, find the charge on the capacitor at any time t > 0.
From the given circuit. Switch S1 is in position A switch S2 is open. Both switches are in these states for a very long time. At t=0, switch S1 moves from position A to B while switch S2 remains open. 10ms after switch S1 moves to position B, switch S2 is closed and remains closed for 20ms only. ANSWER THE FOLLOWING: a.) Expression for the inductor current for 0 ≤ ? < 10??b.) Expression for the inductor current for 10?? ≤ ? < 30?? and 30?? ≤ ? < ∞c.) What is the time (in ms) after switch S1 moves to position B is the current in the inductor equivalent to 30% of the initial value (at ?=0).
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?
The circuit shown below is an underdamped system, and the current through the inductor has the form iL(t)=e^at ( ) (K1sinwt + K2coswt ) for t≥0 a. Determine the numerical values, including signs, of a and w b. If the initial conditions are iL(0) = 1A and Vc (0) =12V , determine the numerical values, including signs, of K1 and K2 c. Using the numbers determined above, write out the complete expression for iL(t)
In the circuit shown below, the switch has been open a long time and the circuit is initially in steady-state. At t=0, the switch is closed. R1=0.2Ω, and R2=0.4Ω. The batteries have EMFs E1=1V and E2=3V. The capacitor has capacitance 10 μF. Hint: What is the voltage on the capacitor just before the switch is closed? Note that there is a voltage drop over the open switch. a) What is the voltage over the capacitor before the switch is closed? b) Draw the Thevenin equivalent circuit as seen by the capacitor. c) What is the time constant for charging the capacitor? d) What is the voltage on the capacitor as a function of time?
In the circuit shown, suppose that the switch has been closed sufficiently long for the capacitor to become fully charged. a) Find the steady-state current through each resistor. b) Find the charge on the capacitor. c) The switch is now opened at t= 0. Write an equation for the current iR2 through R2 as a function of time. d) Find the time that it takes for the charge on the capacitor to fall to 1/5 of its initial value.
16. Consider a simple RC circuit which has a resistor of 2 ohm and capacitor of 3F. If the initial voltage is 12V then find the charge q(t) is expression. 17. Suppose we have a RC circuit with an alternating voltage V(t) = V_{m} * cos(5t) If the initial voltage is 4V and the resistor has a resistance of 8 ohm and the capacitor is of capacitance 2F then find the charge for the circuit ?
In a series circuit capacitor C is being charged through a resistor R using a cell of emf E as in the diagram below. if the current flowing i = dq/dt and the potential across the resistor ER = iR and potential across the capacitor Ec = qC a. derive the differential equation for the circuit b. and determine the solution to the differential equation derived c. suppose a car drives at a speed 4t/2 m/s where t is the time in seconds, how far did the car get in 2 seconds (starting at t = 0) d. and how far did it get in t = 10s
The current, i, through a capacitor depends on time, t, and is given by where V is the voltage across the capacitor and C is the capacitance of the capacitor. Derive an integral expression, in terms of i and C, for the voltage V A capacitor of capacitance 3 x 10-2 F has a current i(t) through it where Determine the function for the voltage across the capacitor The change in current through a semiconductor diode depends on the applied voltage and is given by: where: V = applied voltage (V) I = diode current (A) Is = reverse saturation current (A) T = temperature (K) q and k are constants Given that when V = 0, I = 0 find an expression for the current with voltage. The reverse saturation current for a particular diode is 1 x 10-9 A and at 300 K 40. Write down an expression for the current and find the value of the current when V = 0.35 volts.
Consider a capacitor C discharging through a resistor R, as shown in the figure. a. After how many time constants is the charge on the capacitor one fourth of its initial value?b. As we know, the energy stored in the capacitor decreases with time as it discharges. After how many time constants is this stored energy one fourth of its initial value?c. After how many time constants is the current in the RC circuit half its initial value?d. What is the power dissipated in the resistor during the capacitor discharge process?
(a) Determine the equilibrium charge on the capacitor in the circuit shown as a function of R. (b) Evaluate the charge when R = 10.0 Ω. (c) Can the charge on the capacitor be zero? If so, for what value of R? (d) What is the maximum possible magnitude of the charge on the capacitor? For what value of R is it achieved? (e) Is it experimentally meaningful to take R = ∞? Explain your answer. If so, what charge magnitude does it imply?
Consider the circuit above. The switch has been closed for a very long time before opening at t=0s. Determine the Inductor current (in amperes) right after the switch has been opened, the time constant of the circuit for ?>0 (in ms), and the Expression for the inductor current for ?≥0.

SEE MORE QUESTIONS

Recommended textbooks for you

Power System Analysis and Design (MindTap Course …

Electrical Engineering

ISBN:

9781305632134

Author:

J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:

Cengage Learning