Initial Voltage in an RC circuit with a Current Source and no Voltage Source

[Bassa]

Homework Statement

[/B]
Derive an expression for vc(t) in the circuit of Figure P4.13 and sketch vc(t) to scale versus. I attached a screen shot of the circuit for this problem.

time.

Homework Equations

V = IR
V = V0exp(-t/tau)

The Attempt at a Solution

[/B]
I am trying to find the initial conditions to this problem. To do this, I have said that at t < 0 the capacitor will act as a short circuit for a dc current. we would then have that the current that is going through the resistor R is 10mA. This would yield to Vc(0) = (.01)(2000) = 20V. When I checked a solution of this problem, they get that Vc(0) = 0V. I am not really sure why that is! Thank you very much for your help!

 

[ehild]

Homework Statement

[/B]
Derive an expression for vc(t) in the circuit of Figure P4.13 and sketch vc(t) to scale versus. I attached a screen shot of the circuit for this problem.

View attachment 113412 time.

Homework Equations

V = IR
V = V0exp(-t/tau)

The Attempt at a Solution

[/B]
I am trying to find the initial conditions to this problem. To do this, I have said that at t < 0 the capacitor will act as a short circuit for a dc current. we would then have that the current that is going through the resistor R is 10mA. This would yield to Vc(0) = (.01)(2000) = 20V. When I checked a solution of this problem, they get that Vc(0) = 0V. I am not really sure why that is! Thank you very much for your help!

Short circuit means zero resistance. Would the current flow through the resistor, when it can choose a parallel zero-resistance path?

 

[Bassa]

Short circuit means zero resistance. Would the current flow through the resistor, when it can choose a parallel zero-resistance path?

Thanks you for the quick reply! Oh! I I did not think of it this way. My answer would be "No, it would not." That raises another question that might be related to a fundamental piece of information that I don't know. Current would also not flow if there was no change in voltage, which the resistor offers, right?

 

[ehild]

Thanks you for the quick reply! Oh! I I did not think of it this way. My answer would be "No, it would not." That raises another question that might be related to a fundamental piece of information that I don't know. Current would also not flow if there was no change in voltage, which the resistor offers, right?

Yes, no current through the resistor implies zero voltage across it.
But you can think in the point of view of the capacitor. At t=0, there is zero charge on it. The voltage across a capacitor is V=Q/C. So zero charge means zero voltage across the capacitor, and the resistor and capacitor are parallel connected, so V(t)=0 at t=0.
Is your "relevant equation" V = V0exp(-t/tau) correct then?

 

[Bassa]

Yes, no current through the resistor implies zero voltage across it.
But you can think in the point of view of the capacitor. At t=0, there is zero charge on it. The voltage across a capacitor is V=Q/C. So zero charge means zero voltage across the capacitor, and the resistor and capacitor are parallel connected, so V(t)=0 at t=0.
Is your "relevant equation" V = V0exp(-t/tau) correct then?

So, I think that I am misunderstanding the problem. The arrow on the switch in the diagram means that the switch was closed for a long time and then it was opened at t=0s. If this is the case, then would that not mean that the capacitor was charged at t <= 0?

 

[ehild]

So, I think that I am misunderstanding the problem. The arrow on the switch in the diagram means that the switch was closed for a long time and then it was opened at t=0s. If this is the case, then would that not mean that the capacitor was charged at t <= 0?

If the switch is closed, it means short-circuit for the current source. Why should the current choose a different path?

 

[Bassa]

If the switch is closed, it means short-circuit for the current source. Why should the current choose a different path?

I think I am starting to understand where you are coming from. Initially, I thought that current would not go through the parallel piece of wire because there is no voltage drop there, but it would go to the resistor because there there is a voltage drop and the current could flow. I have always thought that current would not go throw a wire that did not have a voltage drop. I think this is where my misunderstanding is coming from.

 

[gneill]

Moderator's note: Changed the thread title to make it less generic and more specific to the problem being addressed.

 

[Bassa]

Moderator's note: Changed the thread title to make it less generic and more specific to the problem being addressed.

Thank you for the note. I changed the title of the thread.

 

[Bassa]

If the switch is closed, it means short-circuit for the current source. Why should the current choose a different path?

Would the current not choose the path that has a voltage drop, which is the one with the resistor?

 

[gneill]

Would the current not choose the path that has a voltage drop, which is the one with the resistor?

Current *causes* a voltage drop when it flows through a resistor. If it's flowing elsewhere, there will be no voltage drop.

 

[ehild]

Would the current not choose the path that has a voltage drop, which is the one with the resistor?

How do you know that there is a voltage drop across the resistor? The voltage across a resistor is U=IR. The resistor is not connected to a voltage source, the voltage across it is determined by the current. Zero current, zero voltage.
The branch including the closed switch has zero resistance. So the voltage across the current source is zero. So is the voltage across both the resistor and capacitor.

 

[Bassa]

How do you know that there is a voltage drop across the resistor? The voltage across a resistor is U=IR. The resistor is not connected to a voltage source, the voltage across it is determined by the current. Zero current, zero voltage.
The branch including the closed switch has zero resistance. So the voltage across the current source is zero. So is the voltage across both the resistor and capacitor.

Thank you very much for this explanation! I really appreciate it!

 

[Bassa]

Current *causes* a voltage drop when it flows through a resistor. If it's flowing elsewhere, there will be no voltage drop.

Thank you!