RC Circuit Problem: Hi, Is Capacitor Replaced by Short Circuit?

In summary, the conversation discusses the replacement of a capacitor with an open circuit in part b and a short circuit in part c. It is explained that this is done in order to determine the time constant, RC, and the Thevenin resistance. Alternatives to this method, such as solving a differential equation or using Laplace Transforms, are mentioned but deemed less efficient. Ultimately, some form of circuit analysis is necessary to determine the time constant.
  • #1
sammyqw
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Homework Statement


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2. Homework Equations [/B]
KCL, Node Analysis , Mesh Currents

The Attempt at a Solution


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Hi, in part b when t>0 the capacitor is replaced by an open circuit , however in part c the capacitor is replaced by a short circuit why is that?Aren't inductors the only ones replaced by short circuits?
 
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  • #2
sammyqw said:
Hi, in part b when t>0 the capacitor is replaced by an open circuit , however in part c the capacitor is replaced by a short circuit why is that?Aren't inductors the only ones replaced by short circuits?
They were looking for the resistance that the capacitor "sees" in order to determine the time constant, RC. One way to do that is to remove the capacitor and determine the Thevenin resistance as seen at those terminals. The author of the solution decided to find the Thevenin resistance by determining the short circuit current and the open circuit voltage. Divide the voltage by the current and voila, Thevenin resistance. That short circuit for the capacitor is just the application of that method.
 
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  • #3
gneill said:
They were looking for the resistance that the capacitor "sees" in order to determine the time constant, RC. One way to do that is to remove the capacitor and determine the Thevenin resistance as seen at those terminals. The author of the solution decided to find the Thevenin resistance by determining the short circuit current and the open circuit voltage. Divide the voltage by the current and voila, Thevenin resistance. That short circuit for the capacitor is just the application of that method.
Is there any other way to find the same answer that you may know? Thanks for your help.
 
  • #4
sammyqw said:
Is there any other way to find the same answer that you may know? Thanks for your help.
I suppose one could work out and solve a differential equation for the circuit, but that would likely be a lot of work for the same result. Or one could analyze the circuit using Laplace Transforms, again arriving at the same result after more work than necessary.

One way or another, in order to determine the time constant some work has to be done analyzing the circuit. The Thevenin equivalent is a common approach.
 

1. What is an RC circuit?

An RC circuit is a type of electrical circuit that contains both a resistor (R) and a capacitor (C). The resistor controls the flow of current, while the capacitor stores electrical charge.

2. How does a capacitor behave in an RC circuit?

In an RC circuit, the capacitor acts as a temporary storage device for electrical charge. When the circuit is first turned on, the capacitor charges up to the same voltage as the power source. As the capacitor charges, the voltage across it increases and the current decreases.

3. What happens when a capacitor is replaced by a short circuit in an RC circuit?

When a capacitor is replaced by a short circuit in an RC circuit, it essentially becomes a wire with no resistance. This means that the capacitor can no longer store charge and the circuit behaves as if the capacitor is not even there.

4. How does the behavior of an RC circuit change when a capacitor is replaced by a short circuit?

Replacing the capacitor with a short circuit in an RC circuit changes the behavior of the circuit by removing the capacitor's ability to store charge. This results in a higher current flow and a decrease in the time constant, which is the time it takes for the capacitor to charge or discharge.

5. What are some real-world applications of RC circuits?

RC circuits have many practical applications, including in filters, oscillators, and timing circuits. They are also commonly used in electronic devices such as radios, televisions, and computers.

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