RC Circuit Discharge Conceptual Question

[DaleSwanson]

http://i.imgur.com/ZCcaZpq.png

I have the solution manual, so this is more just a question of why, rather than what.

I understand that with the switch open:
v_A = 3v
v_B = v_C = 0v
i₀ = 0.25 mA

When the switch closes it creates a short that makes the two 6kΩ resistors irrelevant. What I don't understand is why anything should change then. The solution manual tells me that a current would flow from the capacitor from B to C, but why? It seems like nodes B and C should be at 0v both before and after the switch is closed.

 

[phinds]

Yes, node B is at zero both before and after the switch is closed, but after the switch is closed, what is the voltage across the capacitor? Is it any different than before the switch is closed?

 

[lewando]

You are right--book is wrong.

 

[DaleSwanson]

As far as I can tell the voltage across the capacitor should always be 3v.

 

[rezeew]

It is important to understand that in an RC circuit, the capacitor is able to store and release charge, while the resistor is able to resist the flow of current. In this particular circuit, when the switch is open, the capacitor is fully charged to 3V and there is no current flowing through the circuit. However, when the switch is closed, a short circuit is created, allowing the capacitor to discharge through the resistor.

Initially, the voltage across the capacitor is 3V, which is higher than the voltage across the resistor (0V), causing a current to flow from the capacitor to the resistor. This current will continue to flow until the voltage across the capacitor has decreased to 0V, at which point the capacitor will be fully discharged and no more current will flow.

The reason why the voltage at nodes B and C changes is because of the change in current flow. Before the switch is closed, there is no current flowing through the circuit, so the voltage at nodes B and C is 0V. However, when the switch is closed, the current flowing through the resistor creates a voltage drop across it, resulting in a non-zero voltage at nodes B and C.

In summary, when the switch is closed, the capacitor begins to discharge through the resistor, causing a change in current flow and resulting in a non-zero voltage at nodes B and C. This is a fundamental concept in RC circuits and is crucial in understanding the behavior of these types of circuits.