RLC Circuits: Determine i(0+), v(0+), i(∞), and v(∞)

[gvc3k]

http://image.cramster.com/answer-board/image/501adeb46c35e1d66d704eb5d3c30ced.jpg

1) Determine: a. The value of i(0+)
b. The value of v(0+)
c. The value of i( ∞)
d. The value of v( ∞)

2) For t > 0, determine: a. The value of http://image.cramster.com/answer-board/image/cramster-equation-2009412031536337421471334550311516.gif
b. The value of http://image.cramster.com/answer-board/image/cramster-equation-2009412032256337421474514237817093.gif
c. The natural response form for the voltages and currents . with undeterminined coefficients.
d. Write the expression for the complete response with . undetermined coefficients
(V(t))
e. Evaluate the coefficients to get v(t)


Any help greatly appreciated, thank you

 

[tiny-tim]

Welcome to PF!

Hi gvc3k! Welcome to PF!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[Mene]

!

1) a. The value of i(0+) would be the initial current in the circuit at time t=0. This can be found by using the initial conditions of the circuit, such as the initial voltage and inductor/capacitor values, and solving for the current using Ohm's law and Kirchoff's laws.
b. The value of v(0+) would be the initial voltage in the circuit at time t=0. This can also be found using the initial conditions and circuit laws.
c. The value of i(∞) would be the steady state current in the circuit once it has reached its equilibrium. This can be found by analyzing the circuit using steady state analysis methods, such as using phasor diagrams.
d. The value of v(∞) would be the steady state voltage in the circuit once it has reached its equilibrium. This can also be found using steady state analysis methods.

2) a. The value of http://image.cramster.com/answer-bo...uation-2009412031536337421471334550311516.gif would be the current in the circuit at t > 0. This can be found by using the differential equation for the circuit and solving for the current at a specific time t.
b. The value of http://image.cramster.com/answer-bo...uation-2009412032256337421474514237817093.gif would be the voltage in the circuit at t > 0. This can also be found using the differential equation and solving for the voltage at a specific time t.
c. The natural response form for the voltages and currents with undetermined coefficients would be in the form of exponential functions, such as e^-at and cos(at) or sin(at), depending on the circuit elements. The coefficients a and b would need to be determined using the initial conditions and circuit laws.
d. The expression for the complete response with undetermined coefficients would involve both the natural response form and the forced response form, which would include any external sources in the circuit. It would be in the form of V(t) = Vn(t) + Vf(t), where Vn(t) is the natural response and Vf(t) is the forced response.
e. The coefficients can be evaluated by plugging in the initial conditions and solving for the undetermined coefficients a and b. Once the coefficients are determined