Find the charge on the plates a long time after the switch is closed

In summary, the goal is to find the charge on the plates of the capacitor a long time after the switch is closed. After some calculations, it is determined that the current leaving the battery is 0.962 A. To find the voltage across the capacitor, this current is multiplied by 27 ohms. The diamond shaped segment of the circuit can be eliminated to simplify the calculations for the steady state regime.
  • #1
Jimmy25
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Homework Statement



I'm having a problem with the circuit in the attached diagram. I am looking for the charge on the plates of the capacitor a long time after the switch is closed.

Homework Equations





The Attempt at a Solution



I found the current leaving the battery is 0.962 A a long time after the switch is closed. The solution says to multiply this by 27 ohms to find the voltage across the capacitor from which the charge can be calculated. I don't understand how this is possible since the diamond shaped segment is a complex circuit.
 

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  • #2
A long time after the switch is closed, we have a steady state regime, that is the capacitors are charged up so no current flows through them. You can simply eliminate them from the circuit(mentally) and then calculate the current and the voltage drops between their plates.

Hope this helps.
 

1. What is the significance of finding the charge on the plates a long time after the switch is closed?

Finding the charge on the plates after a long period of time allows us to understand the behavior of the electric field and how it changes over time. It also gives us insight into the stability and longevity of the system.

2. How does the charge on the plates change over time after the switch is closed?

The charge on the plates will initially increase as the electric field builds up between them. However, as the air molecules surrounding the plates become ionized, the charge on the plates will eventually reach a steady state and remain constant.

3. What factors affect the amount of charge on the plates after the switch is closed?

The amount of charge on the plates is affected by the voltage of the power source, the distance between the plates, and the dielectric material between them. It is also influenced by the conductivity of the surrounding environment and any external factors such as temperature or humidity.

4. Can the charge on the plates ever reach a maximum value and remain constant?

Yes, the charge on the plates will eventually reach a maximum value and remain constant. This is known as the steady state charge and is determined by the capacitance of the system and the voltage of the power source.

5. How can the charge on the plates be calculated or measured after the switch is closed?

The charge on the plates can be calculated using the equation Q = CV, where Q is the charge, C is the capacitance, and V is the voltage. It can also be measured using a device called a coulombmeter, which measures the amount of charge passing through it.

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