What Are the Initial and Steady State Values in an SPST Switched RLC Circuit?

In summary, the conversation discusses finding the values of vC and iL at different time points in a circuit with a closing SPST switch. At t=0-, vC is 12V and iL is 0. At t=0, vC is -3A and vL is 12V. At t=infinity, vC is 0V and iL is 4A. The circuit is a basic one and the person is checking their answers for accuracy.
  • #1
asdf12312
199
1

Homework Statement


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SPST switch closes at t=0. Find vC(0-) and iL(0-), iC(0) and vL(0), and vC(infinity) and iL(infinity).

Homework Equations


The Attempt at a Solution


kind of basic circuit, i know, but i just wanted to check my answers in case i did something wrong.

At t=0- : capacitor acts like open circuit, inductor like short circuit. also there no closed loops, so there's no current. vC(0-)=V(s)=12V, and iL(0-)=0.

at t=0: capaciator behaves like voltage source, inductor like current source of 0A. so would iC(0) be -3A? and vL(0)=12V.

at t=infinity: capacitor acts like open circuit, inductor like short circuit. vC(infinity)=0V, and iL(infinity)=4A.
 
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  • #2
Looks right to me
 
  • #3
anyone else?? did i do this right?
 
  • #4
asdf12312 said:
anyone else?? did i do this right?

Yes you did.
 
  • #5


Your analysis is mostly correct. At t=0, the capacitor will have an initial voltage of 12V, but since it acts like a voltage source, the current through it will depend on the rest of the circuit. In this case, since there is no closed loop, the current through the capacitor will be 0A. Therefore, iC(0) will also be 0A.

At t=infinity, the capacitor will have fully charged to 0V, so vC(infinity) will be 0V. The inductor will also behave like a short circuit, so the current through it will be determined by the voltage source of 12V and the resistance in the circuit. Since the resistance is 3 ohms, the current through the inductor will be 4A, as you correctly stated.

Overall, your analysis is correct, but just be careful with the signs of the currents at t=0. It's always a good idea to double check your calculations to make sure they make sense.
 

FAQ: What Are the Initial and Steady State Values in an SPST Switched RLC Circuit?

1. What is an SPST switch RLC circuit?

An SPST (Single Pole Single Throw) switch RLC circuit is a type of electrical circuit that contains a single switch, a resistor, an inductor, and a capacitor. The switch can be either open or closed, allowing or blocking the flow of electricity through the circuit. This type of circuit is commonly used in electronic devices, such as radios and amplifiers.

2. How does an SPST switch work in an RLC circuit?

When the switch in an SPST RLC circuit is open, no current flows through the circuit. However, when the switch is closed, the current can flow through the circuit and charge the capacitor. The inductor in the circuit will resist this change in current flow, causing the current to oscillate back and forth between the capacitor and the inductor. This results in a resonant circuit, which can have various applications depending on the values of the components.

3. What is the purpose of the resistor in an SPST switch RLC circuit?

The resistor in an SPST RLC circuit serves to limit the current flow through the circuit. Without a resistor, the current would continue to flow back and forth between the capacitor and inductor indefinitely, leading to potential damage to the components. The resistor helps to stabilize the current and prevent any potential harm to the circuit.

4. What are some common uses for SPST switch RLC circuits?

SPST switch RLC circuits have a variety of applications in electronic devices. They can be used in radio receivers to tune into specific frequencies, in amplifiers to control the gain of the signal, and in filters to block unwanted frequencies. They are also commonly used in oscillators and timing circuits.

5. How can I calculate the resonant frequency of an SPST switch RLC circuit?

The resonant frequency of an SPST RLC circuit can be calculated using the formula f = 1 / (2π√(LC)), where f is the resonant frequency in Hertz, L is the inductance in Henrys, and C is the capacitance in Farads. This formula assumes ideal conditions and may need to be adjusted for real-world circuits. Alternatively, there are online calculators available that can help with determining the resonant frequency of an SPST switch RLC circuit.

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