What is the value of the inductor in this capacitor and inductor problem?

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In summary, the conversation discusses a problem involving a capacitor charged by a battery and connected to an inductor. The angular frequency of the resulting oscillation is given and the value of the inductor is being sought. Using the equation ω = 1/sqrt(LC), the value of L is determined to be 2.67 H, which is incorrect. It is discovered that the correct answer is 256 μH, with the caveat that the capacitance of the capacitor is not fully known.
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Chase11
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Homework Statement


A capacitor is charged with a 12 volt battery until there is 3 μc of charge on the capacitor. The capacitor is then connected to an inductor. The angular frequency of the resulting oscillation is 1.25 x 105 rad/s. What is the value of the inductor?

Homework Equations


LC: ω = 1/sqrt(LC)

The Attempt at a Solution


rearranging the equation gives: L=1/(ω2C)=1/(1.25E5rad/sec)(3E-6C)

This gave me an answer of 2.67 H, which is incorrect. Am I not using the correct equation for this type of problem?
 
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  • #2
What do you think C is in the formula for the angular frequency ω = 1/sqrt(LC)??
 
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Hi! Your answer is going to be wrong for two reasons, I think. You've forgotten there's a squared term? The C in the formula is capacitance, not charge.

I'm curious, though --- does your textbook give you its correct answer??
 
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Sorry I know C is for capacitance I don't know why I did that, I still can't figure this out though. What term is supposed to be squared in this equation? It does give me the correct answer, it is supposed to be 256 μH.
 
  • #5
Nevermind I figured it out thanks guys.
 
  • #6
Chase11 said:
the correct answer, it is supposed to be 256 μH.
The problem says the capacitor is given a charge of 3 μC from the battery; though it doesn't state that the capacitor is fully charged to 12V. This tells us that the capacitance is at least a certain minimum value---it could be larger and just not charged right up to 12V. We aren't told exactly.

So IMHO the correct answer is that L ≤ 256μH

This would make a good trick question, allocating 1 mark for 256 uH and 1 mark for the inequality.
 
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FAQ: What is the value of the inductor in this capacitor and inductor problem?

What is a capacitor and how does it work?

A capacitor is an electronic component that stores electrical energy in the form of an electric field. It consists of two conductive plates separated by an insulating material called a dielectric. When a voltage is applied to the capacitor, it charges the plates, creating an electric field between them. The capacitor can then store this energy until it is needed.

What is an inductor and what is its purpose?

An inductor is an electronic component that stores energy in the form of a magnetic field. It consists of a coil of wire wrapped around a core material. When a current flows through the coil, it creates a magnetic field around it. Inductors are used to store energy, regulate current, and filter out unwanted signals in electronic circuits.

What is the relationship between capacitors and inductors in a circuit?

Capacitors and inductors are complementary components in a circuit. They have opposite effects on the flow of current, with capacitors storing energy and inductors resisting changes in current. Together, they form a resonant circuit that can store and transfer energy efficiently.

How do you solve a capacitor/inductor problem in a circuit?

To solve a capacitor/inductor problem in a circuit, you need to use the principles of electrical circuit analysis. This involves using Kirchhoff's circuit laws, Ohm's law, and other equations to determine the voltage, current, and power in the circuit. It is important to keep track of the polarity and direction of current flow in capacitors and inductors to properly analyze the circuit.

What are some common applications of capacitors and inductors?

Capacitors and inductors have a wide range of applications in electronic circuits. Capacitors are commonly used in power supply circuits, filter circuits, and timing circuits. Inductors are used in power converters, audio and video equipment, and communication systems. They are also essential components in many electronic devices such as computers, televisions, and smartphones.

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