Solve RC Circuit Problem: R1=10k, R2=15k, C=0.4F, V=20V

[terryds]

Homework Statement

R1 = 10 kohms
R2 = 15 kohms
C = 0.4F
Voltage source = 20 V

At first, the switch is closed for a long time so that the capacitor reach its steady-state condition. Then, the switch is opened at t=0. How much does the current flow across R_2 at t= 4ms?

Homework Equations

I = I₀ e^(-t/RC)

The Attempt at a Solution

I'm a bit confused about the voltage of capacitor at t=0. Is it equal to the voltage source? Or, is it equal to the voltage at R_2 resistor since it's in parallel with it (by using the voltage divider at loop 1, we get the voltage at R_2)?

 

[ehild]

Homework Statement

View attachment 113566

R1 = 10 kohms
R2 = 15 kohms
C = 0.4F
Voltage source = 20 V

At first, the switch is closed for a long time so that the capacitor reach its steady-state condition. Then, the switch is opened at t=0. How much does the current flow across R_2 at t= 4ms?

Homework Equations

I = I₀ e^(-t/RC)

The Attempt at a Solution

I'm a bit confused about the voltage of capacitor at t=0. Is it equal to the voltage source? Or, is it equahat do you thikl to the voltage at R_2 resistor since it's in parallel with it (by using the voltage divider at loop 1, we get the voltage at R_2)?

What do you think? Does current flow through the resistors, when the switch is closed? What would be that current if the voltage across the capacitor was the same as that of the voltage source?

 

[terryds]

What do you think? Does current flow through the resistors, when the switch is closed? What would be that current if the voltage across the capacitor was the same as that of the voltage source?

I don't think the current flows through the resistors when it's closed since the current will go for the capacitor first.
If the voltage across the capacitor was the same of the voltage source there'll be no current flow since it has been fully charged.
Is it correct? Please help me.

 

[ehild]

I don't think the current flows through the resistors when it's closed since the current will go for the capacitor first.

But the problem says that the switch is closed for a long time, so the voltage across the capacitor reaches its steady state value. Does current flow through the capacitor then? Does current flow through the resistors at the same time?

If the voltage across the capacitor was the same of the voltage source there'll be no current flow since it has been fully charged.
Is it correct? Please help me.

No current where?

 

[terryds]

But the problem says that the switch is closed for a long time, so the voltage across the capacitor reaches its steady state value. Does current flow through the capacitor then? Does current flow through the resistors at the same time?

No current where?

At steady state, no current flow through the capacitor, but there is current flowing through the resistors.
So, no current through the capacitor, but there is current through the resistor.
Is it correct?
Anyway, what's the capacitor voltage? I think it'll be equal to voltage through R_2. Am I right?

 

[ehild]

At steady state, no current flow through the capacitor, but there is current flowing through the resistors.
So, no current through the capacitor, but there is current through the resistor.
Is it correct?
Anyway, what's the capacitor voltage? I think it'll be equal to voltage through R_2. Am I right?

Yes, everything is right

 

[terryds]

Yes, everything is right

May I ask some more?
Before reaching the steady state condition (switch is closed), does the current flow through R_1 and R_2?
If there is a resistor next to the switch, does the current flow through it?
And, why current favors capacitors over resistors?

 

[ehild]

May I ask some more?
Before reaching the steady state condition (switch is closed), does the current flow through R_1 and R_2?
If there is a resistor next to the switch, does the current flow through it?
And, why current favors capacitors over resistors?

At the instant when the switch gets closed, all current flows across the capacitor, charging it. As the capacitor gets more and more charged, the voltage increases across it. As it is connected parallel with R2, there is the same voltage across R2, and current must flow across the resistor. At the same time, there is potential difference across R1, so current flows across R1, too.

 

[terryds]

At the instant when the switch gets closed, all current flows across the capacitor, charging it. As the capacitor gets more and more charged, the voltage increases across it. As it is connected parallel with R2, there is the same voltage across R2, and current must flow across the resistor. At the same time, there is potential difference across R1, so current flows across R1, too.

If there is a resistor next to the switch (in series), will the current flow through it? (before reaching steady-state and the switch is closed)
How come the current just 'jump' through the capacitor without passing through the resistor first? Why the current is not split up when it meets the junction to the capacitor and the resistor?

 

[ehild]

If there is a resistor next to the switch (in series), will the current flow through it? (before reaching steady-state and the switch is closed)
How come the current just 'jump' through the capacitor without passing through the resistor first? Why the current is not split up when it meets the junction to the capacitor and the resistor?

At the instant when the switch gets closed, the capacitor is like a short-circuit. The same current flows across it and across R1. As charge builds up the source current is shared between the capacitor and R2, and the sum of these currents flows through R1.