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

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Homework Help Overview

The discussion revolves around an RC circuit problem involving two resistors (R1 = 10 kΩ, R2 = 15 kΩ), a capacitor (C = 0.4 F), and a voltage source (V = 20 V). The scenario describes the behavior of the circuit when the switch is closed for a long time, allowing the capacitor to reach a steady-state condition, and then opened at t=0. Participants are trying to determine the current flow across R2 at a specific time after the switch is opened.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants express confusion regarding the voltage across the capacitor at t=0 and whether it equals the voltage source or the voltage across R2. There are questions about current flow through the resistors when the switch is closed and the implications of the capacitor being fully charged.

Discussion Status

There is an ongoing exploration of the behavior of current in the circuit both before and after the switch is opened. Some participants suggest that at steady state, while no current flows through the capacitor, current does flow through the resistors. Others are questioning the nature of current flow in relation to the capacitor and resistors, indicating a productive dialogue without a clear consensus yet.

Contextual Notes

Participants are discussing the implications of the circuit's steady-state behavior and the assumptions regarding current flow through the components. There is a focus on understanding the initial conditions and the effects of the switch's position on the circuit dynamics.

terryds
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Homework Statement


16930509_837738609701988_943157630_o.jpg


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)?
 
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terryds said:

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?
 
ehild said:
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.
 
terryds said:
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?
terryds said:
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?
 
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ehild said:
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?
 
terryds said:
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 :smile:
 
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ehild said:
Yes, everything is right :smile:
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?
 
terryds said:
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.
 
ehild said:
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?
 
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terryds said:
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.
 
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