How does a resonant LC tank circuit oscillate at its resonant frequency?
1 Answer
A resonant LC tank circuit oscillates at its resonant frequency due to the interplay between the inductance (L) and capacitance (C) elements within the circuit. When properly designed and excited, the tank circuit can store and exchange energy between the inductor and capacitor at the resonant frequency, resulting in sustained oscillations.
Let's dive into the process of how this happens:
Charging the Capacitor:
Initially, let's assume that the capacitor in the LC tank circuit is charged, and there is no current flowing through the inductor. The voltage across the capacitor is at its maximum, and the current through the inductor is at its minimum.
Discharging the Capacitor:
Once the capacitor is fully charged, we disconnect the power source, and the only pathway for the electric charge to flow is through the inductor. As the capacitor discharges, it starts to supply current to the inductor.
Current in the Inductor:
The inductor opposes changes in current flow, so as the current begins to flow through the inductor, the inductor starts building up a magnetic field around it. This magnetic field stores energy.
Capacitor Energy Transferred to Inductor:
As the capacitor continues to discharge, the energy stored in the capacitor's electric field is transferred to the inductor's magnetic field. The voltage across the capacitor decreases, while the current flowing through the inductor increases.
Capacitor Current Reversal:
At a specific moment, the capacitor will be fully discharged, and the current will be at its maximum through the inductor. This point is where the polarity of the voltage across the capacitor changes. The voltage across the capacitor and the current through the inductor are now in opposite directions.
Energy Exchange:
As the current in the inductor reaches its maximum, the inductor's magnetic field stores the maximum amount of energy, while the voltage across the capacitor is at its minimum. At this moment, the energy in the system is almost entirely in the form of magnetic energy in the inductor.
Magnetic Field Collapse and Capacitor Recharging:
The inductor now begins to release its stored energy back into the circuit as the magnetic field collapses. The collapsing magnetic field induces a voltage in the circuit in the same direction as the original voltage across the capacitor. This causes the capacitor to recharge, but in the opposite direction.
Repeat Cycle:
The process repeats, and the energy starts to oscillate between the inductor's magnetic field and the capacitor's electric field. As long as there is no significant energy loss in the circuit, the oscillations will continue at the resonant frequency determined by the values of the inductance and capacitance.
It's important to note that in a real-world circuit, there will be some resistance and other losses that can dampen the oscillations over time. However, in an idealized scenario with no losses, the LC tank circuit will continue to oscillate indefinitely at its resonant frequency.
Let's dive into the process of how this happens:
Charging the Capacitor:
Initially, let's assume that the capacitor in the LC tank circuit is charged, and there is no current flowing through the inductor. The voltage across the capacitor is at its maximum, and the current through the inductor is at its minimum.
Discharging the Capacitor:
Once the capacitor is fully charged, we disconnect the power source, and the only pathway for the electric charge to flow is through the inductor. As the capacitor discharges, it starts to supply current to the inductor.
Current in the Inductor:
The inductor opposes changes in current flow, so as the current begins to flow through the inductor, the inductor starts building up a magnetic field around it. This magnetic field stores energy.
Capacitor Energy Transferred to Inductor:
As the capacitor continues to discharge, the energy stored in the capacitor's electric field is transferred to the inductor's magnetic field. The voltage across the capacitor decreases, while the current flowing through the inductor increases.
Capacitor Current Reversal:
At a specific moment, the capacitor will be fully discharged, and the current will be at its maximum through the inductor. This point is where the polarity of the voltage across the capacitor changes. The voltage across the capacitor and the current through the inductor are now in opposite directions.
Energy Exchange:
As the current in the inductor reaches its maximum, the inductor's magnetic field stores the maximum amount of energy, while the voltage across the capacitor is at its minimum. At this moment, the energy in the system is almost entirely in the form of magnetic energy in the inductor.
Magnetic Field Collapse and Capacitor Recharging:
The inductor now begins to release its stored energy back into the circuit as the magnetic field collapses. The collapsing magnetic field induces a voltage in the circuit in the same direction as the original voltage across the capacitor. This causes the capacitor to recharge, but in the opposite direction.
Repeat Cycle:
The process repeats, and the energy starts to oscillate between the inductor's magnetic field and the capacitor's electric field. As long as there is no significant energy loss in the circuit, the oscillations will continue at the resonant frequency determined by the values of the inductance and capacitance.
It's important to note that in a real-world circuit, there will be some resistance and other losses that can dampen the oscillations over time. However, in an idealized scenario with no losses, the LC tank circuit will continue to oscillate indefinitely at its resonant frequency.