Charges must flow from source around loop back to source {circuit, electricity}| {electric circuit, flow}. At circuit points, current that goes in must equal current that comes out. Voltages around circuit loops must add to zero. Otherwise, electron density increases somewhere in circuit.
Earth {ground, electricity}|, or conductor leading to Earth, is an electron sink. Earth has many molecules and can absorb or give any number of charges without changing potential.
Circuit current and voltage follow laws {Kirchoff's laws} {Kirchoff laws}. Kirchoff's laws apply to circuit steady state. Transiently, Kirchoff's laws can break.
At circuit points, current coming in equals current going out. If current flowing in did not equal current flowing out, charge builds or falls at point and repels or attracts incoming charges, to make net charge return to zero.
Around circuit loops, voltages add to zero. If voltages around loop do not add to zero, extra voltage sends more charges to low-voltage point and so makes sum of voltages become zero again.
Wave-front amplitude or phase modifications {modulation, electricity}| can carry information on carrier waves. Information can vary amplitude {amplitude modulation, circuit} (AM) or frequency {frequency modulation, circuit} (FM). Frequency modulation carries temporal information along propagation line. Amplitude modulation carries spatial information perpendicular to propagation line.
Circuits {short circuit}| can have almost no resistance, allowing very high current.
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.
Circuit loads can be on separate wires {parallel circuit}|. Loads split currents. Voltages are equal. If circuit voltage sources are on separate wires, currents add, and voltages are equal. For resistances in parallel, resistance reciprocals add to equal total-resistance reciprocal, because cross-sectional area is more. Capacitances in parallel add, because area is more. For inductances in parallel, inductance reciprocals add to equal total-inductance reciprocal, because area is more.
Circuit loads can be in same wire {series circuit}|. Currents through loads are equal. Loads split voltages. If circuit voltage sources are in same wire, currents through loads are equal and voltages add. Resistances in series add, because length is longer. For capacitances in series, capacitance reciprocals add to equal total-capacitance reciprocal, because distance is more. Inductances in series add, because length is more.
Two circuits {coupled circuit} can share impedance, allowing energy transfer.
Circuits {filter circuit} can transmit frequency range, while blocking other frequencies. Filter circuits can remove frequency range, while allowing other frequencies, by differentiating or averaging. Circuits can choose different frequencies {selectivity, filter}. Frequency filtering sharpens edges, because edges have high frequency, and blurs have low frequency.
Circuits {LC circuit} can have inductor and capacitor. Energy flows from inductance magnetic field to capacitance electric field and then from capacitance electric field to inductance magnetic field, at resonance frequency. In resonating circuits, capacitance and inductance reactances are equal, so total reactance equals zero.
Circuits {RC circuit} can have resistor and capacitor. Voltage V depends on time t: V = Vo * e^(-t / (R*C)). Switching on circuit makes voltage build up in capacitor as field builds. Current lags behind voltage. At voltage alternation frequency, circuit resonates.
Circuits {RL circuit} can have inductance and resistor. Current I depends on time t: I = Io * e^(-t * R / L). At switching on, current changes fast, so voltage in coil is high. Then current becomes constant so voltage goes to zero, and current lags behind voltage. At current-alternation frequency, circuit resonates.
Thermionically emitted electrons can travel in beams, under side-electromagnet control, to fluorescent screens, where they excite phosphor crystals to make light {cathode ray tube}|. Cathode ray tubes are in TVs and oscilloscopes.
Circuit devices {detector} can select one signal from several.
Solid-state semiconductor circuit elements or vacuum tubes {diode}| can allow current to flow in only one direction. Diodes change alternating current to direct current. Tubes can have cathode emitter and anode plate. If plate is positive, emitted electrons flow toward plate. If plate is negative, no emitted electrons flow. For solid state, np junction allows charge to flow only in one direction, from P-type to N-type, with high resistance in other direction.
Circuit devices {mixer, signal} {electric circuit, mixer} can combine frequency signals.
Circuit devices {oscillator, circuit}| {electric oscillator} can change voltage waveform to other frequencies and amplitudes.
Devices {rectifier}| can change alternating to direct current.
Devices {rheostat}| can make variable resistance.
Circuit devices {wave shaper} can change voltage waveform.
Sunlight electric potential can make electric current in materials {photocell}|.
Shining light onto selenium {selenium cell} increases conductivity, because light increases electric field.
Instruments {ammeter}| can measure currents.
Instruments {galvanometer}| can measure small currents and current direction.
Instruments {ohmmeter}| can measure resistance.
Instruments {potentiometer}| can measure voltages at zero current, as ratio to exactly known voltage.
Instruments {voltmeter}| can measure electric potentials.
Devices {Wheatstone bridge}| can find resistance or capacitance in circuits using ratios. Wheatstone bridges eliminate voltage effects. AC current negates overall flow effects.
Current from a potential source P splits between two known resistances, R1 and R2, which have a galvanometer G across their endpoints to measure current and voltage (Figure 1). From one endpoint is an adjustable resistance Rv. From the other endpoint is an unknown resistance Rx. The resistances Rv and Rx meet at a point. If the ratio of the adjustable resistance Rv to the first known resistance R1 equals the ratio of the unknown resistance Rx to the second known resistance R2, the galvanometer has zero voltage and current.
For typical resistances, one can set R1 = R2, so Rv = Rx at galvanometer zero current and voltage.
If three resistances are known and one unknown, the measured voltage allows calculating the unknown resistance.
Wheatstone bridges can also find capacitance.
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Date Modified: 2022.0225