Two EE questions - nodal analysis and circuit modeling

[ming2194]

Two EE questions -- nodal analysis and circuit modeling

Homework Statement

Homework Equations

I was given R1, R2, and Iα(t), the time for the switch to closed (50μs<=t<=100μs)
The question is asking about the energy associated with 2 sources and dissipated in R1, R2.

The Attempt at a Solution

For the 1st question, part should be ok for me. But i have no idea on how to start the part b).take integration for Iα(t) (since Iα(t)=da/dt) , then obtain a i=(-1/5)e^-500t
but what value for the integrals? integrated from t = 50μs to 100μs? or from t = 0μs to 200μs ? then "I" can be found?
E=Pt, = (IV)t. What value of t will be used here for each source and resistor to find the energy?

For Q4, totally no idea on it. It is about the topic of diode?

 

[NascentOxygen]

In Q3, once you know the voltage & current associated with each element, the product of the two will be its power. Integration of power leads to energy.

Q4 does call for a diode arrangement.

 

[ming2194]

In Q3, once you know the voltage & current associated with each element, the product of the two will be its power. Integration of power leads to energy.

Q4 does call for a diode arrangement.

Thanks so much for your reply.
After calculation I find ：
I1： 2/7(ia)
I2: 5/7（ia)
I3= -5/7 ia
V1= 20/7 （ia）
V2= 100/7 ia

Then , power of R1 = v1 i1
I get 4000/49 e^-5000t
Then I need to integral it to find energy but what should I set for the upper and Lower intergal? Since the switch is closed for 50u<T< 100u, but the question asks for the energy for 0<T<200u， so which range should I use ？
And why?

 

[NascentOxygen]

You will have to evaluate the integral in pieces, until you have covered the full interval. The circuit changes when R2 is shorted out.