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.
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).
AC Phase Relationships
CIVIL: C leads V (capacitor), V leads I in L (inductor)
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.
C
Capacitor
I
Current leads
V
Voltage
I
In inductors
L
Voltage leads current
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.
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.
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.
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.
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.
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 = -NΔΔ/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.
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.
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.
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
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
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
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.
Max E-field the dielectric can withstand before it fails
🎓 Common Exam Questions
Q: State and explain Kirchhoff's two circuit laws.
A: Kirchhoff's Current Law (KCL): the sum of all currents entering a node equals the sum of all currents leaving it — conservation of charge. No charge builds up at a junction. Kirchhoff's Voltage Law (KVL): the sum of all voltage drops around any closed loop equals zero — conservation of energy. The energy gained from sources equals energy lost across resistors, capacitors, etc. Together KCL and KVL allow analysis of any circuit no matter how complex. Method: label unknown currents, write KCL at each node, write KVL for each independent loop, solve the system of equations.
Q: Explain how a transformer works and derive the voltage ratio.
A: A transformer uses electromagnetic induction to change AC voltage levels. An AC current in the primary coil creates a changing magnetic flux in the iron core. By Faraday's Law, this changing flux induces an EMF in the secondary coil. Voltage ratio: V_s/V_p = N_s/N_p where N is the number of turns. Step-up transformer: N_s > N_p → higher voltage. Step-down: N_s < N_p → lower voltage. By conservation of energy (ideal transformer): V_p I_p = V_s I_s — higher voltage means lower current. Real transformers have efficiency losses from eddy currents, hysteresis, and resistance. Used in power transmission — high voltage, low current means less I²R loss over long distances.
Q: Derive the energy stored in a capacitor and explain where the energy is stored.
A: A capacitor stores charge Q on plates separated by distance d with capacitance C = Q/V. Energy stored: U = ½QV = ½CV² = Q²/2C. Derivation: to add a small charge dq against voltage V = q/C requires work dW = V dq = (q/C)dq. Integrating from 0 to Q: W = Q²/2C. The energy is stored in the electric field between the plates. Energy density of electric field: u = ½ε₀E². Similarly, an inductor stores energy ½LI² in its magnetic field with energy density u = B²/2μ₀. In an LC circuit, energy oscillates between electric (capacitor) and magnetic (inductor) forms — like a mass on a spring oscillating between kinetic and potential energy.
Q: What is electromagnetic induction and how does it lead to Faraday's and Lenz's Laws?
A: Electromagnetic induction: a changing magnetic flux through a circuit induces an EMF (voltage). Faraday's Law: EMF = −dΦ_B/dt where Φ_B = ∫B·dA is the magnetic flux. The EMF is proportional to the rate of change of flux — faster change means larger EMF. Lenz's Law (from the negative sign): the induced current flows in a direction that opposes the change in flux that caused it — conservation of energy (if it aided the change, it would create a runaway amplification violating energy conservation). Applications: electric generators (mechanical energy → electrical), transformers, induction motors, wireless charging, metal detectors. Motional EMF: a conductor moving through a magnetic field generates EMF = BLv.
Q: Explain RC circuits — charging, discharging, and the time constant.
A: RC circuit charging: when a voltage V₀ is applied, charge builds on the capacitor exponentially. V_C(t) = V₀(1 − e^(−t/τ)) where τ = RC is the time constant. Current: I(t) = (V₀/R)e^(−t/τ) — starts at maximum, decays to zero. After one τ: capacitor is 63% charged. After 5τ: essentially fully charged (99%). RC discharging: V_C(t) = V₀e^(−t/τ). Current flows in reverse until capacitor is empty. The time constant τ = RC determines how quickly the circuit responds. Large R or C → slow response. Applications: timing circuits, filters (RC acts as low-pass or high-pass filter depending on where output is taken), signal smoothing, camera flash circuits.