RC, RL, and RLC circuits have reactance and resistance vector sum {impedance}|. Voltage equals impedance times current. Maximum power has equal source and circuit impedances.
Inductance and capacitance {reactance}| aid or impede current flow by storing and releasing energy, without heat loss.
comparison
Resistance opposes current and has heat loss.
phase
Reactance causes lag between voltage and current. In inductors, high frequency makes big current change and so large voltage. High inductance makes current changes make big voltage changes. Inductive reactance R equals two times pi times frequency f times inductance L: R = 2 * pi * f * L. In capacitors, high frequency makes voltage stay low, because little charge can build up. High capacitance requires large charge to make voltage, so voltage stays low. Capacitive reactance R equals reciprocal of two times pi times frequency f times capacitance C: R = 1 / (2 * pi * f * C).
Electrical devices {capacitor} {capacitance}| can store electrical energy. Electric-energy storage ability C is charge Q divided by voltage V: C = Q / V. Capacitance C equals material dielectric strength d times length l divided by cross-sectional area A: C = d * l / A.
field
In capacitors, electric field stores energy E: E = 0.5 * Q * V = 0.5 * C * V^2.
current
Electric-field energy builds as current flows. Electric-field energy tends to push current out. Current I is capacitance C times voltage change dV over time change dt: I = (1 / C) * dV / dt. Current and voltage are out of phase.
parallel plates
In parallel-plate capacitors, capacitance C equals electric permittivity e times dielectric constant k times cross-sectional area A divided by distance d between plates: C = e * k * A / d. Electric field between plates is constant and perpendicular to plates. If plates are farther apart, charge separation is more, voltage is more, and capacitance is less. If plate area is larger, charges spread out more, voltage is less, and capacitance is more. If dielectric constant is greater, material between plates has more polarization, field is less, voltage is less, and capacitance is more.
examples
Disk capacitors and rod capacitors work like parallel-plate capacitors. Two aluminum pie plates can make capacitor. Leyden jars can store charge as capacitance. Electrolytic capacitors allow only one-way current.
Circuits with current can store magnetic energy {inductance}|. Circuit devices {inductor} can store magnetic energy. Inductors are wire coils, so current makes strong magnetic field down coil middle. Soft iron bar can be in middle.
energy
Energy stored depends on current change compared to voltage. Inductance L is voltage V divided by current change dI with time change dt: L = V / (dI/dt). V = L * dI/dt. Magnetic-field energy builds as current flows. Magnetic-field energy tends to push current to stop. Current and voltage are out of phase. Magnetic-field energy E equals half inductance L times current I squared: E = 0.5 * L * I^2.
factors
Inductance increases as coil area increases, current-change frequency decreases, space magnetic-permeability increases, current decreases, voltage increases, coil-turn number decreases, and inductor length increases.
mutual inductance
Two coils with current have mutual inductance.
5-Physics-Electromagnetism-Circuit
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Date Modified: 2022.0225