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Compare energy storage in inductors and capacitors.
Inductors store energy in a magnetic field; capacitors store energy in an electric field.
Compare the time constant of an LR circuit to the angular frequency of an LC circuit.
LR circuit time constant: \( \tau = L/R \). LC circuit angular frequency: \( \omega = \frac{1}{\sqrt{LC}} \)
Compare the initial behavior of an inductor and a capacitor in a DC circuit.
Initially, an inductor acts like an open circuit, while a capacitor acts like a short circuit.
Compare the formulas for energy stored in an inductor and a capacitor.
Inductor: \( U = \frac{1}{2}LI^2 \). Capacitor: \( U = \frac{1}{2}CV^2 \)
Compare LR and LC circuits.
LR circuits exhibit exponential current changes; LC circuits exhibit sinusoidal oscillations.
What is the effect of increasing the number of loops in an inductor coil?
Increases the inductance (L).
What is the effect of increasing the core size of an inductor?
Increases the inductance (L).
What happens when current changes rapidly through an inductor?
A large induced EMF opposes the change in current.
What happens when you connect an inductor and capacitor in series?
The circuit oscillates, with energy transferring between the inductor's magnetic field and the capacitor's electric field.
What is the effect of adding a resistor to an LC circuit?
The oscillations are damped, and energy is dissipated as heat.
What is the effect of doubling the current in an inductor?
The energy stored in the inductor quadruples.
What is inductance (L)?
The proportionality constant between magnetic flux and current, measured in Henries (H). \( \Phi_B = LI \)
What is an inductor?
A coil of wire that resists changes in current and stores energy in a magnetic field.
Define magnetic flux (\(\Phi_B\)).
A measure of the amount of magnetic field lines passing through a given area.
What is the time constant (\(\tau\)) in an LR circuit?
The time it takes for the current in an LR circuit to reach approximately 63.2% of its maximum value. \( \tau = L/R \)
Define angular frequency (\(\omega\)) in an LC circuit.
The rate at which energy oscillates between the capacitor and inductor in an LC circuit. \( \omega = \frac{1}{\sqrt{LC}} \)
What is induced EMF?
The electromotive force generated in a circuit due to a changing magnetic field. \( \varepsilon = -L \frac{dI}{dt} \)