Glossary
Angular Frequency (of LC Circuits)
The rate of oscillation of charge and current in an LC circuit, determined by the inductance (L) and capacitance (C).
Example:
A higher angular frequency means the LC circuit oscillates faster, completing more cycles per second.
Capacitors
Electronic components that store electrical energy in an electric field between two conductive plates.
Example:
A camera flash charges a capacitor to quickly release a burst of light for illumination.
Conservation of Energy (in LC Circuits)
The principle that the total energy (sum of electric and magnetic potential energy) in an ideal LC circuit remains constant over time.
Example:
Even as energy shifts between the capacitor and inductor, the conservation of energy ensures the total energy in the circuit never changes, assuming no resistance.
Damped oscillations
Oscillations whose amplitude gradually decreases over time due to energy dissipation, typically caused by resistance in the circuit.
Example:
If a real LC circuit has some resistance, the charge and current will exhibit damped oscillations, eventually fading to zero as energy is lost as heat.
Electric Potential Energy (in Capacitor)
The energy stored in the electric field of a capacitor, proportional to the square of the voltage across it.
Example:
When an LC circuit's capacitor is fully charged, all the circuit's energy is temporarily stored as electric potential energy.
Energy Transfer (in LC Circuits)
The continuous oscillation of energy between the electric field of the capacitor and the magnetic field of the inductor in an LC circuit.
Example:
In an oscillating LC circuit, energy transfer occurs as energy constantly swaps between being fully stored in the capacitor's electric field and then fully in the inductor's magnetic field.
Inductors
Electronic components that store energy in a magnetic field when current flows through them, opposing changes in current.
Example:
An inductor in a power supply can smooth out current fluctuations, preventing sudden spikes.
Kirchhoff's loop rule (as applied to LC circuits)
A fundamental circuit law stating that the sum of voltage drops around any closed loop in a circuit must be zero, used to derive the differential equation for LC oscillations.
Example:
Applying Kirchhoff's loop rule to an LC circuit allows us to write a differential equation that describes how charge and current change over time.
LC Circuits
Electrical circuits consisting of an inductor (L) and a capacitor (C) that exhibit oscillations of charge and current.
Example:
Radio tuners often utilize LC circuits to select specific frequencies from incoming electromagnetic waves.
Magnetic Potential Energy (in Inductor)
The energy stored in the magnetic field of an inductor, proportional to the square of the current flowing through it.
Example:
At the moment of maximum current in an LC circuit, all the energy is temporarily stored as magnetic potential energy within the inductor.
Maximum Current Calculation (in LC Circuits)
The process of determining the peak current in an LC circuit by equating the maximum energy stored in the capacitor to the maximum energy stored in the inductor.
Example:
To perform a maximum current calculation in an LC circuit, you can set the initial stored energy in the capacitor equal to the maximum energy the inductor will hold.
Period of Oscillation (in LC Circuits)
The time it takes for one complete cycle of charge and current oscillation in an LC circuit.
Example:
A longer period of oscillation means the LC circuit takes more time to complete one full swing of energy transfer.
Phase constant (in SHM equation for charge)
A parameter ($\phi$) in the sinusoidal equation for charge in an LC circuit that determines the initial state (charge at t=0) of the oscillation.
Example:
If a capacitor is fully charged at t=0, its phase constant would typically be zero in the cosine function for charge.
Simple Harmonic Motion (in LC Circuits)
The sinusoidal oscillation of charge and current in an ideal LC circuit, analogous to a mass on a spring.
Example:
The charge on the capacitor in an LC circuit follows simple harmonic motion, meaning it varies smoothly like a sine or cosine wave over time.