Electricity, Circuits, and Magnetism

Electrical concepts appear regularly on the OAR MCT. You do not need advanced electrical engineering knowledge — focus on Ohm's Law, circuit types, and basic component behavior.

Fundamental Electrical Quantities

The Water Analogy

Think of electricity like water flowing through pipes:

• Voltage is the pressure pushing water through
• Current is the amount of water flowing per second
• Resistance is how narrow or blocked the pipe is
• Higher pressure (voltage) pushes more water (current) through
• A narrower pipe (higher resistance) reduces flow (current)

Ohm's Law

V = I × R

This is the most important electrical equation for the OAR.

Example: A circuit has a 12V battery and a 4Ω resistor. What is the current? I = V/R = 12/4 = 3 A

Example: A 2A current flows through an 8Ω resistor. What voltage is across the resistor? V = IR = 2 × 8 = 16 V

Series Circuits

Components are connected end-to-end in a single path.

Series Rules

Example: Three resistors (2Ω, 3Ω, 5Ω) are connected in series to a 20V battery.

• R_total = 2 + 3 + 5 = 10Ω
• I = V/R = 20/10 = 2A (same through all)
• V across 2Ω: V = IR = 2 × 2 = 4V
• V across 3Ω: V = IR = 2 × 3 = 6V
• V across 5Ω: V = IR = 2 × 5 = 10V
• Check: 4 + 6 + 10 = 20V ✓

Series Circuit Facts

• If one component breaks, the entire circuit stops (think: old Christmas lights)
• Larger resistors drop more voltage
• Adding more resistors decreases total current

Parallel Circuits

Components are connected side-by-side, each with its own path to the power source.

Parallel Rules

Example: Two resistors (6Ω and 3Ω) are in parallel with a 12V battery.

• 1/R_total = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2 → R_total = 2Ω
• I_total = 12/2 = 6A
• I through 6Ω: I = 12/6 = 2A
• I through 3Ω: I = 12/3 = 4A
• Check: 2 + 4 = 6A ✓

Parallel Circuit Shortcut (Two Resistors)

R_total = (R₁ × R₂) / (R₁ + R₂)

Example: 4Ω and 12Ω in parallel: R_total = (4 × 12)/(4 + 12) = 48/16 = 3Ω

Parallel Circuit Facts

• If one branch breaks, others continue working (think: modern house wiring)
• Total resistance is ALWAYS less than the smallest individual resistor
• Adding more branches decreases total resistance and increases total current

Series vs. Parallel Comparison

Electrical Power

P = I × V = I²R = V²/R

Example: A 120V appliance draws 5A. What power does it consume? P = 120 × 5 = 600 W

Example: What is the resistance of a 100W light bulb at 120V? R = V²/P = 120²/100 = 14,400/100 = 144Ω

Key Components

Capacitors

• Store electrical energy in an electric field
• Charge up when connected to a voltage source, discharge when the source is removed
• Block DC current but pass AC current
• In series: 1/C_total = 1/C₁ + 1/C₂ (opposite of resistors!)
• In parallel: C_total = C₁ + C₂ (opposite of resistors!)

Inductors

• Resist changes in current using a magnetic field
• Oppose increases in current when energized, oppose decreases when de-energized
• Pass DC current but resist AC current (opposite of capacitors)

Transformers

• Change voltage levels using electromagnetic induction
• V₁/V₂ = N₁/N₂ (voltage ratio equals turns ratio)
• Step-up transformer: increases voltage, decreases current
• Step-down transformer: decreases voltage, increases current
• Power is conserved: V₁I₁ = V₂I₂

Magnetism

Key Concepts

• Electric current creates a magnetic field
• Moving a conductor through a magnetic field generates voltage (electromagnetic induction)
• Electromagnets: coils of wire with current produce magnetic fields; more turns = stronger field
• Permanent magnets: like poles repel, opposite poles attract