Glossary
Energy Dissipation
The process by which electrical energy is converted into other forms, primarily heat, within a circuit, often occurring in resistors.
Example:
When you use a toaster, the heating elements demonstrate energy dissipation as they convert electrical energy into the heat needed to toast bread.
Exponential Curves
Mathematical functions that describe the time-dependent changes in current, voltage, or stored energy in LR circuits during their transient phase.
Example:
The charging of a capacitor or the current build-up in an inductor typically follows exponential curves, approaching a final value asymptotically.
Inductors
Passive electrical components that store energy in a magnetic field when electric current flows through them, and resist changes in current.
Example:
An inductor in a car's ignition system helps create a high-voltage spark by rapidly collapsing its magnetic field when the current is interrupted.
Kirchhoff's Loop Rule
A fundamental principle stating that the algebraic sum of the potential differences (voltages) around any closed loop in a circuit must be zero.
Example:
To analyze the voltage drops across components in a complex circuit, you would apply Kirchhoff's Loop Rule to each closed path.
LR Circuits
Electrical circuits composed of resistors and inductors, which exhibit time-dependent behavior due to the inductor's resistance to changes in current.
Example:
When you turn on a speaker, the internal LR circuit might cause a slight delay before the sound fully kicks in as the current builds up in the inductor.
Lenz's Law
States that the direction of an induced electromotive force (EMF) or current is such that it opposes the change in magnetic flux that produced it.
Example:
When you quickly push a magnet into a coil, the induced current creates a magnetic field that opposes the motion, demonstrating Lenz's Law.
Resistors
Circuit components that oppose the flow of electric current, converting electrical energy into heat.
Example:
In a simple flashlight, the bulb acts as a resistor, converting electrical energy from the battery into light and heat.
Steady State
The condition in an LR circuit reached after a long time (much greater than the time constant), where current and voltage have stabilized and no longer change, and the inductor acts like a simple wire.
Example:
After a long time, the current in an LR circuit reaches its steady state, behaving as if only the resistor and battery are present.
Time Constant (τ)
A characteristic time scale for an LR circuit, defined as L/R, which indicates how quickly the current or voltage in the circuit reaches its steady state.
Example:
If an LR circuit has a small time constant, it will reach its maximum current much faster than a circuit with a large one.
Time-Dependent Behavior
The characteristic of a circuit where current, voltage, or other quantities change over time, typically due to the presence of energy-storing components like inductors or capacitors.
Example:
The gradual brightening of an LED connected to an LR circuit after a switch is closed illustrates the time-dependent behavior of the current.
Transient State
The initial period in an LR circuit after a change (like closing a switch), during which current and voltage are changing rapidly and the inductor's properties are time-dependent.
Example:
Immediately after a switch is closed in an LR circuit, the current is in a transient state, gradually increasing from zero.