Proven Mnemonics & Acronyms — fast to learn, hard to forget.
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Series vs Parallel
Series: same current everywhere. Parallel: same voltage across each branch.
Series vs Parallel
The one rule that unlocks all circuit analysis
Series: current identical through all components, voltages add. Parallel: voltage identical across all branches, currents add. Christmas lights in series — one fails, all fail.
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🃏 Series vs Parallel
Series vs parallel circuits — what stays the same?
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🃏 Answer
Series: same current everywhere. Parallel: same voltage across each branch.
Series: current identical through all components, voltages add. Parallel: voltage identical across all branches, currents add. Christmas lights in series — one fails, all fail.
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Magnetic Force Direction
Right-hand rule: fingers point in current direction, curl to B-field, thumb = force
Magnetic Force Direction
Find the direction of magnetic force on a current or moving charge
Point fingers in direction of velocity (or current), curl toward B-field → thumb points in direction of magnetic force on a positive charge. Flip hand for electrons (negative charge).
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🃏 Magnetic Force Direction
Right-hand rule — how do you find the magnetic force?
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🃏 Answer
Right-hand rule: fingers point in current direction, curl to B-field, thumb = force
Point fingers in direction of velocity (or current), curl toward B-field → thumb points in direction of magnetic force on a positive charge. Flip hand for electrons (negative charge).
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AC Phase Relationships
CIVIL: in a Capacitor (C), current (I) leads voltage (V); voltage (V) leads current (I) in an inductor (L)
AC Phase Relationships
Capacitor and inductor phase relationships — one mnemonic covers both
In a Capacitor: Current leads Voltage. In an inductor (L): Voltage leads Current. CIVIL encodes both. Crucial for AC circuit analysis and power factor calculations.
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🃏 AC Phase Relationships
CIVIL — what leads what in capacitors and inductors?
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🃏 Answer
CIVIL: in a Capacitor (C), current (I) leads voltage (V); voltage (V) leads current (I) in an inductor (L)
CCapacitor
ICurrent leads
VVoltage
IIn inductors
LVoltage leads current
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Electrical Power
P = IV = I²R = V²/R — electrical power in three useful forms
Electrical Power
Three equivalent expressions for electrical power — pick whichever fits
P = IV: power equals current times voltage. P = I²R: useful when you know current and resistance. P = V²/R: useful when you know voltage and resistance. Units: Watts = Joules/second.
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🃏 Electrical Power
Electrical power — the three forms of the formula?
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🃏 Answer
P = IV = I²R = V²/R — electrical power in three useful forms
P = IV: power equals current times voltage. P = I²R: useful when you know current and resistance. P = V²/R: useful when you know voltage and resistance. Units: Watts = Joules/second.
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Coulomb's Law
Coulomb's Law: F = kq₁q₂/r². Like charges repel. Opposite charges attract.
Coulomb's Law
The electric force between charges — mirrors Newton's gravity
F = kq₁q₂/r² where k = 8.99×10⁹ N·m²/C². Like charges (both + or both -): repel. Unlike charges (+ and -): attract. Inverse square law — double distance → ¼ the force. Much stronger than gravity at atomic scales.
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🃏 Coulomb's Law
Coulomb's law?
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🃏 Answer
Coulomb's Law: F = kq₁q₂/r². Like charges repel. Opposite charges attract.
F = kq₁q₂/r² where k = 8.99×10⁹ N·m²/C². Like charges (both + or both -): repel. Unlike charges (+ and -): attract. Inverse square law — double distance → ¼ the force. Much stronger than gravity at atomic scales.
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Electric Fields
Electric field: E = F/q. Field lines go from + to -. Closer lines = stronger field.
Electric Fields
The force per unit charge surrounding any charged object
Electric field E = Force/charge = F/q. Units: N/C or V/m. Field lines originate at positive charges and terminate at negative. Denser field lines = stronger field. A positive test charge would follow the field lines. Uniform field between parallel plates: E = V/d.
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🃏 Electric Fields
Electric field — formula and field-line rules?
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🃏 Answer
Electric field: E = F/q. Field lines go from + to -. Closer lines = stronger field.
Electric field E = Force/charge = F/q. Units: N/C or V/m. Field lines originate at positive charges and terminate at negative. Denser field lines = stronger field. A positive test charge would follow the field lines. Uniform field between parallel plates: E = V/d.
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Kirchhoff's Laws
Kirchhoff's Laws: junction rule (currents in = currents out). Loop rule (voltage gains = voltage drops).
Kirchhoff's Laws
Two rules for analyzing complex circuits
Junction rule (KCL): at any junction, the sum of currents entering equals the sum leaving — conservation of charge. Loop rule (KVL): around any closed loop, the sum of all voltage changes equals zero — conservation of energy. Together they let you solve any circuit.
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🃏 Kirchhoff's Laws
Kirchhoff's two laws?
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🃏 Answer
Kirchhoff's Laws: junction rule (currents in = currents out). Loop rule (voltage gains = voltage drops).
Junction rule (KCL): at any junction, the sum of currents entering equals the sum leaving — conservation of charge. Loop rule (KVL): around any closed loop, the sum of all voltage changes equals zero — conservation of energy. Together they let you solve any circuit.
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Capacitors
Capacitor stores charge: C = Q/V. Energy = ½CV². In series: 1/C total = 1/C₁ + 1/C₂.
Capacitors
How capacitors store energy in an electric field
Capacitance C = Q/V (charge stored per volt). Unit: Farads (F). Parallel plate capacitor: C = ε₀A/d. Energy stored = ½CV² = ½QV. Series capacitors: reciprocals add (like parallel resistors). Parallel capacitors: values add directly (like series resistors). Capacitors block DC, pass AC.
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🃏 Capacitors
Capacitors — capacitance, energy, and series rule?
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🃏 Answer
Capacitor stores charge: C = Q/V. Energy = ½CV². In series: 1/C total = 1/C₁ + 1/C₂.
Capacitance C = Q/V (charge stored per volt). Unit: Farads (F). Parallel plate capacitor: C = ε₀A/d. Energy stored = ½CV² = ½QV. Series capacitors: reciprocals add (like parallel resistors). Parallel capacitors: values add directly (like series resistors). Capacitors block DC, pass AC.
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Electromagnetic Induction
Magnetic flux: Φ = BAcosθ. Faraday's law: changing flux induces EMF. Lenz's law: induced current opposes change.
Electromagnetic Induction
How changing magnetic fields create electric currents
Faraday's law: EMF = -ΔΦ/Δt. More loops (N turns): EMF = -NΔΦ/Δt. Lenz's law: the induced current flows in a direction to oppose the change in flux that created it. Applications: electric generators, transformers, induction cooktops, MRI machines.
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🃏 Electromagnetic Induction
Magnetic flux, Faraday's law, Lenz's law?
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🃏 Answer
Magnetic flux: Φ = BAcosθ. Faraday's law: changing flux induces EMF. Lenz's law: induced current opposes change.
Faraday's law: EMF = -ΔΦ/Δt. More loops (N turns): EMF = -NΔΦ/Δt. Lenz's law: the induced current flows in a direction to oppose the change in flux that created it. Applications: electric generators, transformers, induction cooktops, MRI machines.
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Resistor Combinations
Resistors in series: R total = R₁ + R₂ + R₃. In parallel: 1/R total = 1/R₁ + 1/R₂ + 1/R₃.
Resistor Combinations
How to find total resistance in series and parallel circuits
Series: resistances simply add. Current is the same through all. Voltage divides proportionally. Parallel: reciprocals add. Voltage is the same across all. Current divides inversely proportionally. Total resistance always less than smallest individual resistor in parallel.
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🃏 Resistor Combinations
Resistors in series vs parallel — the formulas?
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🃏 Answer
Resistors in series: R total = R₁ + R₂ + R₃. In parallel: 1/R total = 1/R₁ + 1/R₂ + 1/R₃.
Series: resistances simply add. Current is the same through all. Voltage divides proportionally. Parallel: reciprocals add. Voltage is the same across all. Current divides inversely proportionally. Total resistance always less than smallest individual resistor in parallel.
How transformers change voltage using electromagnetic induction
Transformer works only on AC — changing current creates changing magnetic field which induces voltage in secondary coil. Turns ratio determines voltage ratio. Power conserved (ideal): P = V₁I₁ = V₂I₂. Step up voltage → step down current. Used in power transmission: high voltage, low current = less energy lost.
Transformer works only on AC — changing current creates changing magnetic field which induces voltage in secondary coil. Turns ratio determines voltage ratio. Power conserved (ideal): P = V₁I₁ = V₂I₂. Step up voltage → step down current. Used in power transmission: high voltage, low current = less energy lost.
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Magnetic vs Electric Fields
EVEM — Electric field lines start on positive, end on negative. Magnetic field lines form closed loops — no monopoles.
Key differences between E-fields and B-fields
Electric field lines have sources and sinks; magnetic field lines are always closed loops
Electric field: created by charges, points away from positive and toward negative, field lines begin and end on charges. Magnetic field: created by moving charges or currents, field lines always form closed loops (no magnetic monopoles ever found). Gauss's law for E: flux through closed surface = enclosed charge / ε₀. Gauss's law for B: flux through any closed surface = 0 (always — because no monopoles).
E-field lines
Start on + charge, end on − charge — can be open
B-field lines
Always closed loops — no start or end point
No monopoles
Magnetic north always paired with south — never isolated
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🃏 Magnetic vs Electric Fields
Electric vs magnetic field lines — how do they differ (EVEM)?
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Electric vs magnetic field lines — EVEM
EVEM — Electric field lines start on positive, end on negative. Magnetic field lines form closed loops — no monopoles.
E-field linesStart on + charge, end on − charge — can be open
B-field linesAlways closed loops — no start or end point
No monopolesMagnetic north always paired with south — never isolated
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Maxwell's Equations Summary
GAME — Gauss (E), Ampere, Magnetic Gauss, Faraday — four laws that unify electromagnetism
The four fundamental equations of electromagnetism
Maxwell unified electricity, magnetism, and optics — light is an electromagnetic wave
Gauss's Law (E): electric flux through closed surface = Q_enclosed / ε₀. Gauss's Law (B): magnetic flux through any closed surface = 0. Faraday's Law: changing magnetic flux induces EMF — basis of generators. Ampere-Maxwell Law: currents AND changing electric fields create magnetic fields — Maxwell added the displacement current term. Together they predict electromagnetic waves traveling at c = 1/√(ε₀μ₀).
Gauss (E)
Charges create electric fields — sources and sinks
Faraday
Changing B creates E — basis of generators and inductors
Ampere-Maxwell
Currents AND changing E create B — predicts EM waves
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🃏 Maxwell's Equations Summary
GAME — Maxwell's four equations?
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🃏 Answer
GAME — Gauss (E), Ampere, Magnetic Gauss, Faraday — four laws that unify electromagnetism
Gauss (E)Charges create electric fields — sources and sinks
FaradayChanging B creates E — basis of generators and inductors
Ampere-MaxwellCurrents AND changing E create B — predicts EM waves
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Inductors and Inductance
Inductor opposes CHANGE in current — like inertia for electricity
Self-inductance — the tendency to resist changes in current flow
An inductor stores energy in its magnetic field and fights any change in current
Inductance L measured in Henries. EMF = −L(dI/dt) — the induced EMF opposes the change (Lenz's Law). Energy stored = ½LI². RL circuit time constant τ = L/R — current rises to 63% of final value in one τ. Inductors in series: L_total = L₁ + L₂. In parallel: 1/L_total = 1/L₁ + 1/L₂ (opposite of resistors). At DC steady state: inductor acts as a short circuit (wire). At high frequency AC: inductor acts as open circuit.
Opposes change
EMF = -L dI/dt — fights increases and decreases in current
Energy stored
½LI² — in the magnetic field (not electric like capacitor)
DC steady state
Acts as wire — no changing current, no induced EMF
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🃏 Inductors and Inductance
What does an inductor oppose?
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🃏 Answer
Inductor opposes CHANGE in current — like inertia for electricity
Opposes changeEMF = -L dI/dt — fights increases and decreases in current
Energy stored½LI² — in the magnetic field (not electric like capacitor)
DC steady stateActs as wire — no changing current, no induced EMF
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Dielectrics and Capacitance
Dielectric increases capacitance by factor κ — MORE charge stored at SAME voltage
How inserting an insulator between capacitor plates changes its properties
A dielectric increases capacitance, decreases electric field, and increases energy storage
Capacitance with dielectric: C = κε₀A/d where κ is the dielectric constant (always ≥ 1). κ = 1 for vacuum, ~80 for water, ~2-4 for common insulators. Effect: same voltage → more charge stored (C increases). Same charge → lower voltage (E decreases). Energy stored: U = Q²/2C = ½CV². Dielectric breakdown: if E-field exceeds dielectric strength, insulator fails — this limits maximum voltage. Polarization: dielectric molecules align with field, partially canceling the applied field → weaker net field.