So I had this question on a quiz that I bombed and I'm still confused over it.


What is the steady-state value of the capacitor voltage v(infinity) when excited by the unit step function source?

The way I went around the problem was to find ib(t) which is ib(t) = 5/(4 +1) = 1 A.

I then used the ib(t) to find the voltage source which would be the voltage at infinity (with the capacitor replaced by an open circuit)
Therefore the voltage should be V = 12ib(t) = 12 (1) = 12 V.

I was wrong and I'm not sure why.

Thanks.

PS: Was I wrong in assuming the Rth would be 100 ohms since the left half of the circuit would not contribute?

 

If the cap is fully charged and modeled as an open circuit, like you did, then the dependent current source is not part of a complete circuit, then there is no current.

If I am right, then the Vo(t) is voltage across the 4 Ohm resistor, which is Vo(t)=4*5/(4+1)=4 volt.

 

If the cap is fully charged and modeled as an open circuit, like you did, then the dependent current source is not part of a complete circuit, then there is no current.

If I am right, then the Vo(t) is voltage across the 4 Ohm resistor, which is Vo(t)=4*5/(4+1)=4 volt.

Hmm that's sorta threw me in a loop; Regardless, the options were a. 2.4V b. 1 V c. 9.6 V and d. 0V

I remember picking 9.6 V but can't remember why.

 

Hmm that's sorta threw me in a loop; Regardless, the options were a. 2.4V b. 1 V c. 9.6 V and d. 0V

I remember picking 9.6 V but can't remember why.

Ok, so you picked 9.6 volt first time and it was wrong, I did 4 volt but it is not even a choice, you also did 12 volt and it is also not a choice.

I think it leaves only 0 volt. I am not sure I have a good explanation.

 

Isn't the magnitude of the UNIT step function equal to 1?

That would make Ib=0.2 and Vo= 0.2*12 = 2.4 V.

 

Isn't the magnitude of the UNIT step function equal to 1?

That would make Ib=0.2 and Vo= 0.2*12 = 2.4 V.

Could you please explain how you got your current ib as 0.2? Did you get this information from the graph?

 

1Ω+4Ω=5Ω
(1V)/5Ω=0.2A

 

Isn't the magnitude of the UNIT step function equal to 1?

That would make Ib=0.2 and Vo= 0.2*12 = 2.4 V.

Yes, that makes sense. I need to double check the definition of unit step.

 

The problem says that the voltage is a unit step for questions 1-3 and a 5 V pulse for question 4. But you never give any hint regarding which question it is you are trying to answer. But if you are using a unit step, then you need to consider what the magnitude is of a "unit" step function.