Q: LC Circuit: Q0 = 18 C & I = 0 - What is the Equilibrium Charge?

In summary, the equilibrium charge of an LC circuit with a Q0 of 18 C and no current flow is 18 C. It is calculated using the equation Q = CV, where Q is the charge, C is the capacitance, and V is the voltage. Changes in the initial charge, capacitance, or voltage will affect the equilibrium charge. Over time, the equilibrium charge will remain constant as the circuit reaches a steady state. The equilibrium charge is significant in measuring the energy stored in the circuit and determining the resonant frequency, making it important in applications such as filters and oscillators.
  • #1
gtman12
1
0
At t = 0, Q0 = 18 C and I = 0 in an LC circuit.

(a) At the first moment when the energy is shared equally by the inductor and the capacitor, what is the charge on the capacitor?
 
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  • #2
What have you tried on this? Start by writing the equation of potential drops around the circuit.
 
  • #3


The equilibrium charge in an LC circuit refers to the charge on the capacitor when the system is in a steady state, meaning there is no change in the energy or charge over time. In this case, at t = 0, the initial charge on the capacitor is Q0 = 18 C and the current is I = 0. This means that the capacitor is fully charged and there is no current flowing through the circuit.

At the first moment when the energy is shared equally between the inductor and capacitor, the charge on the capacitor will be equal to half of the initial charge, which is 9 C. This is because in an LC circuit, the energy oscillates between the inductor and capacitor, and at this moment, the energy is equally distributed between the two components.

It is important to note that this equilibrium charge is only reached at this specific moment, and the charge on the capacitor will continue to oscillate between 0 and Q0 as the energy continues to transfer between the inductor and capacitor. The equilibrium charge is not a constant value, but rather a momentary state in the oscillation of the energy in the LC circuit.
 

1. What is the equilibrium charge of an LC circuit with a Q0 of 18 C and no current flow?

The equilibrium charge of an LC circuit is the amount of electric charge that remains on the capacitor when the circuit is in a steady state. In this case, with a Q0 of 18 C and no current flow, the equilibrium charge will also be 18 C.

2. How is the equilibrium charge calculated in an LC circuit?

The equilibrium charge in an LC circuit is calculated using the equation Q = CV, where Q is the charge, C is the capacitance, and V is the voltage. In this case, the voltage is 0, so the equilibrium charge is simply the capacitance (C) multiplied by the initial charge (Q0).

3. What factors affect the equilibrium charge in an LC circuit?

The equilibrium charge in an LC circuit is affected by the initial charge (Q0), the capacitance (C), and the voltage (V). Changes in any of these variables will result in a change in the equilibrium charge.

4. How does the equilibrium charge change over time in an LC circuit?

In an LC circuit, the equilibrium charge will oscillate between the capacitor and inductor, resulting in a sinusoidal pattern. As the circuit reaches a steady state, the equilibrium charge will remain constant.

5. What is the significance of the equilibrium charge in an LC circuit?

The equilibrium charge in an LC circuit is an important measure of the energy stored in the circuit. It is also a key factor in determining the resonant frequency of the circuit, which is important in many applications such as filters and oscillators.

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