Understanding Charge Transfer in C & 2C Circuit

In summary, the conversation discusses the relationship between capacitance and inductance in a circuit, with the variables q_1 and q_2 representing the charge on respective capacitors, and t representing time. The question is whether the current, represented by i_1 and i_2, would be affected by both capacitors. The answer is no, as the short circuit effectively creates two isolated loops, preventing current from straying between them.
  • #1
arpon
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Homework Statement


upload_2015-1-2_19-52-17.png
[/B]
[itex]C[/itex] and [itex]2C[/itex] represent the capacitance of the respective capacitors. [itex]L[/itex] and [itex]2L[/itex] represent the inductance of the respective inductors. Let, the charge on the capacitors GM and PM be [itex]q_1[/itex] and [itex]q_2[/itex] which are variable. [itex]t[/itex] represents time. Initially (when the switch k was closed and [itex]t = 0[/itex]) , [itex]q_1 = \frac{2q_0}{3} ; q_2 = \frac{q_0}{3}[/itex]. Would it be,
[itex]i_1 = - \frac{dq_1}{dt} ; i_2 = - \frac{dq_2}{dt} [/itex] ?
Explain your answer.

Homework Equations


That is conceptual question. No equation is needed.

The Attempt at a Solution


The actual homework was different. But I need to clear my concept before solving the actual problem. My confusion is, the MGHJ segment (which has the current [itex]i_1[/itex]) is connected with both the capacitors. So, won't both the capacitor affect the current [itex]i_1[/itex] ?
 
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  • #2
The short circuit between M and J when the switch is closed effectively creates two isolated loops as no potential can develop across the short. In other words, M and J become a single node. No current from either loop can stray into the other loop past that short circuit.
 
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  • #3
gneill said:
The short circuit between M and J when the switch is closed effectively creates two isolated loops as no potential can develop across the short. In other words, M and J become a single node. No current from either loop can stray into the other loop past that short circuit.
So, if I change the circuit into the following , I think [itex]i_1[/itex] and [itex]i_2[/itex] won't change. Am I right?
upload_2015-1-2_21-11-15.png
 
  • #4
Right.
 
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  • #5


I would like to clarify that the current i_1 is affected by both capacitors in the circuit. This is because the capacitors are connected in series, meaning that the same current flows through both of them. Therefore, the charge on each capacitor will affect the current i_1.

In this specific scenario, the initial charge on the capacitors (q_1 and q_2) will affect the current i_1 at t=0. As time passes, the charge on the capacitors will change and the current i_1 will also change accordingly. Therefore, the equations i_1 = - \frac{dq_1}{dt} ; i_2 = - \frac{dq_2}{dt} are correct, as they represent the rate of change of charge and therefore the current in the circuit.

I hope this clarifies your confusion and helps you in solving the actual problem. It is important to understand the concept of charge transfer in circuits in order to accurately solve problems and make predictions.
 
1.

What is charge transfer in C & 2C circuits?

Charge transfer in C & 2C circuits refers to the movement of electrical charge from one component to another within a circuit. This can occur in various forms, such as the flow of electrons through wires or the buildup of static electricity on a capacitor.

2.

Why is understanding charge transfer important in circuit design?

Understanding charge transfer in circuit design is crucial because it allows engineers to predict and control the flow of electricity within a circuit. This helps ensure that the circuit functions properly and can prevent damage to components due to excessive or unintended charge transfer.

3.

What factors influence charge transfer in C & 2C circuits?

The amount of charge transferred in a circuit is influenced by several factors, including the voltage applied to the circuit, the resistance of the components, and the capacitance of any capacitors present. Additionally, the type of material used for wires and components can also affect charge transfer.

4.

How does charge transfer impact the performance of a circuit?

The amount and direction of charge transfer can significantly impact the performance of a circuit. For example, if too much charge is transferred, it can cause components to overheat or fail. On the other hand, insufficient charge transfer can result in a circuit not functioning at all.

5.

What techniques are used to measure and analyze charge transfer in C & 2C circuits?

There are various techniques used to measure and analyze charge transfer in circuits, including the use of multimeters, oscilloscopes, and simulation software. These tools allow scientists and engineers to observe and quantify the flow of charge in a circuit and make adjustments to optimize its performance.

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