Ohm's Law
VIR Triangle: V = IR
Ohm's Law
Cover what you want to find in the VIR triangle
V (Volts) = I (Amps) × R (Ohms). Cover V → I×R. Cover I → V/R. Cover R → V/I. The foundation of every circuit problem.
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.
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.
Transformers
Transformer: V₁/V₂ = N₁/N₂. Step-up: more secondary turns → higher voltage. Step-down: fewer turns → lower voltage.
Transformers
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.