Impulse function applied to RLC circuit

In summary, the conversation discusses an example from the book "Signals and Systems" by Haykin, where a voltage source with the value of Vo*delta(t) is applied to a series RLC circuit. The question is what is the value of the current i(t) at time t=0+, and the answer given is Io = Vo/L. However, there is confusion about how this is possible, as it seems that there would be no current flow due to the characteristics of the inductor and capacitor. It is suggested to write the differential equation and integrate it to find the value of Io.
  • #1
marc.orr
3
0
Hello, I've been reviewing some material from my undergraduate studies. In the book "Signals and Systems" by Haykin in the first chapter he gives an example of a voltage source with the value of Vo*delta(t) applied to a series RLC circuit.

Vo is some arbitrary constant and delta(t) is the impulse function. The question is what is the value of the current i(t) at time t=0+ where 0+ is at 0 looking from the more positive side of time.

He says the answer is (without any sort of derivation) Io = Vo/L. How is this possible? I figure that as there is an instantaneous change in voltage, the inductor will look like a short circuit and the capacitor will look like an open circuit. So how can there be any current flow?

Thankyou in advance.

Marc
 
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  • #2
marc.orr said:
I figure that as there is an instantaneous change in voltage, the inductor will look like a short circuit and the capacitor will look like an open circuit.
You have this reversed.
 
  • #3
If you write the differential equation and integrate it between 0- and 0+ you can find Io.
 

1. What is an impulse function applied to an RLC circuit?

An impulse function is a mathematical concept used to model a sudden, short-lived change or "impulse" in a system. When applied to an RLC circuit, it represents a brief, powerful electrical signal that can cause a temporary disturbance in the circuit's behavior.

2. How is an impulse function applied to an RLC circuit?

To apply an impulse function to an RLC circuit, a short, high-voltage pulse is sent through the circuit. This pulse acts as the "impulse" and can be achieved using a variety of methods, such as a sudden switch closure or a high-voltage capacitor discharge.

3. What is the purpose of using an impulse function in an RLC circuit?

An impulse function can be used to study the transient behavior of an RLC circuit, meaning its behavior immediately after being subjected to a sudden change. By analyzing the circuit's response to the impulse, we can gain insight into its overall behavior and make adjustments to improve its performance.

4. What types of RLC circuits can an impulse function be applied to?

An impulse function can be applied to a wide range of RLC circuits, including series circuits, parallel circuits, and series-parallel circuits. It can also be used to study circuits with both DC and AC power sources.

5. Are there any limitations to using an impulse function in an RLC circuit?

One limitation of using an impulse function is that it only provides information about the circuit's behavior in the immediate aftermath of the impulse. To fully understand the circuit's behavior over time, additional analysis and experimentation may be necessary.

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