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.

 

[rezeew]

I would suggest starting by reviewing the concepts of nodal analysis and circuit modeling. Nodal analysis is a method used to solve for unknown voltages in a circuit by applying Kirchhoff's current law at each node. Circuit modeling involves representing a real-world circuit with a simplified mathematical model in order to analyze its behavior.

For the first question, it seems like you have a good understanding of how to approach part a), but you may need to clarify what the question is asking for in part b). Are you being asked to find the energy dissipated in R1 and R2 over a specific time interval? If so, you can use the equation E=Pt, where P is the power dissipated in the resistor and t is the time interval. To find the power, you can use the equation P=I^2R, where I is the current and R is the resistance.

For Q4, it is difficult to provide a response without more context. It would be helpful to know what specific topic in diode electronics the question is related to. However, in general, diodes are electronic components that only allow current to flow in one direction. They can be used in circuit modeling to represent non-linear behavior. I would suggest reviewing the basics of diode behavior and diode circuits to approach this question.