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2. Assume steady-state conditions exist at 0. (a) Find the differential equation for it(t) for t>...
Solve for v(t), t>0. a. Find the initial conditions. b. Write the differential equation. c. Find the general form of the solution. d. Find the coefficients of the solution by matching the initial conditions. t=0 100V 0.22 } 1F + 0.25H3
State Equations, initial conditions, and differential equation solution R1 t 0 V0-20V R 1-20? L-2mH VO R2 The switch in the circuit has been closed a long time, and is opened at t = 0' Find the capacitor voltage, V.(t), for t20; in the cases: (a) R2-102; (b) R2-1002; (c) R2-87/17? Hint: Find the initial conditions, then treat the circuit as an RLC circuit via its differential equation
Find the Steady State Voltage and Current Values. Develop the equation for i(t) , the current through the inductor and Vout(t). I need help, I don't know if my calculations are correct, I found the neper frequency to be: a=439.109 rad/sec and resonant frequency to be Wo=14586.5 rad/sec. This is a parallel step response RLC circuit The circuit is underdamped. Please show all work clearly so that I can understand the process. Vout(t) is the voltage across R2 (which is...
+ Problem 6 The input to the circuit is is(t) =2 + 4u(t) A. a. Determine the voltage v(t) across the left-handed 32 resistor for t > 0. b. Plot and fully label v(t) and interpret the result. 3Ω v(t) 3Ω 3 2 0.25 H Problem 7 Find the complete response of the capacitor v(t) for t > 0 for the circuit. Assume the circuit is at steady state at t 0. t=0 42 1 H + 6V 1/4 F...
(2) The circuit is at steady state for t<0. Find v(t) for t>0. Answer t=0 ZF Navt)14 T
3) RLC Parallel Circu its: Differential Equations and Laplace U2 U1 TOPEN 0 TCLOSE 0 CL1 R1 0.15H C1 2E-8F 1 10E-3 2 J 10E-3 Att-0, U1 closes and U2 opens. 3.1: What is the intial (t-0+) current through the capacitor? What is the inital (t-0+) voltage across the capacitor? 3.2: What is the DC steady state current though the capacitor as t goes to infinity? 3.3: Find the current through the CAPACITOR as a function of time for R...
Please do the problem if you can do ALL parts. t-0 a SW1 SW2 0.5 Ω 2 1Ω V. R3 20 A T v(t) 0.5 F 0.5 H 0 Find the initial current i(0) through the inductor and the initial voltage v(0) across the capacitor at t 0. b. Write a node equation at node a fort2 0. c. Represent v(t) as a function of i(t) on the series connection of R2 and L. Find dv(t)/dt. Derive a second-order differential...
A. Write down the differential equation describing the circuit for an arbitrary time-dependent voltage V (t), in terms of the inductance L, capacitance C and resistance R of the circuit. B. Determine an analytic solution when the voltage is switched off [V(t) = ol. First, express your solution in terms of arbitrary coefficients as appropriate. Then, determine those coefficients for the initial conditions where the current is given by I(に0)-10 and satisfies I'(t = 0) = 0. C. Determine the...
A. Write down the differential equation describing the circuit for an arbitrary time-dependent voltage V (t), in terms of the inductance L, capacitance C and resistance R of the circuit. B. Determine an analytic solution when the voltage is switched off [V(t) = ol. First, express your solution in terms of arbitrary coefficients as appropriate. Then, determine those coefficients for the initial conditions where the current is given by I(に0)-10 and satisfies I'(t = 0) = 0. C. Determine the...
For the following circuit, steady state conditions exist at tco. The switch is closed at t-0. Given R1-0.68kO, R-1.8ko, C-0.SuF, and Vi-12 V (a) Write the differential equation with Vc as independent variable for o (10 points) (b) Determine the initial and final conditions (10 points) (c) Find time constant using equivalent resistance method. Verify the time constant is the same as from differential equation (10 points) Rs Vi