Energy stored in a LC circuit

In summary, when the current is flowing in the circuit, all the energy is stored in the inductor. When the current stops, it is because all the energy has been transferred to the capacitor. To find the fraction of energy stored in the inductor when the capacitor is half charged, we can use the equations 1/2 *Q^2/C = U of capacitor and 1/2 * LI^2 = U of inductor. By setting the initial total energy as U, we can determine the maximum charge associated with it, and then use the equation 1/8Q^2/C + x*LI^2 = U to find the fraction of energy stored in the inductor when the capacitor is half charged.
  • #1
Luek
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Homework Statement


Energy in the circuit remains constant. When the current is flowing, the energy stored is all stored in the inductor. When the current stops flowing, it is because all the energy is stored in the capacitor.
Find the fraction of energy stored in the inductor when half of the max charge is on the capacitor.

L = inductor
C = capacitor
I = current

Homework Equations


1/2 *Q^2/C = U of capacitor
1/2 * LI^2 = U of inductor

The Attempt at a Solution


[/B]
Didn't know where to really go.

1/2 *Q^2/C + 1/2 * LI^2 = U
Q= .5Q
1/8Q^2/C + x*LI^2 =U
x= 7/8?
 
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  • #2
When all the energy is in the capacitor (maximum charge) there is no energy in the inductor (current is zero). So start by positing some initial total energy U and determine the maximum charge associated with it. What happens when that charge is reduced to half and current is flowing?
 

Related to Energy stored in a LC circuit

1. What is a LC circuit?

A LC circuit, also known as a tank circuit, is an electrical circuit that contains an inductor (L) and a capacitor (C) connected in parallel. It is used to store and release electrical energy in the form of oscillations.

2. How does energy get stored in a LC circuit?

When a voltage is applied to a LC circuit, the capacitor stores the energy in the form of an electric field, while the inductor stores the energy in the form of a magnetic field. This back and forth transfer of energy between the capacitor and inductor creates oscillations and results in energy being stored in the circuit.

3. What is the formula for calculating the energy stored in a LC circuit?

The formula for calculating the energy stored in a LC circuit is E = 1/2 * L * I2 = 1/2 * Q2 / C, where E is the energy stored, L is the inductance, I is the current, Q is the charge, and C is the capacitance.

4. How does the energy stored in a LC circuit affect the oscillation frequency?

The energy stored in a LC circuit is directly proportional to the oscillation frequency. This means that the more energy that is stored, the higher the frequency of the oscillations will be. This can be seen in the formula for calculating the oscillation frequency, f = 1 / (2 * π * √(LC)), where L is the inductance and C is the capacitance.

5. What are some real life applications of LC circuits?

LC circuits have many practical applications, such as in radio and television transmitters, electric power grid systems, and electronic oscillators. They are also used in electronic filters and tuning circuits, as well as in medical equipment such as MRI machines and defibrillators.

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