Electric charge (symbol Q) is measured in Coulombs (C). It is the fundamental property that causes electromagnetic interactions. Electrons carry a negative charge; protons carry a positive charge.
Electric current (symbol I) is the rate of flow of charge past a point. It is measured in Amperes (A).
Conventional vs Electron Flow
- Conventional current flows from positive (+) to negative (−) — this is the direction used in circuit analysis.
- Electron flow is in the opposite direction: from − to +.
- Both conventions are correct in their own context. Exam questions use conventional current unless stated otherwise.
DC vs AC
| Type | Description | Example |
|---|---|---|
| Direct Current (DC) | Charge flows in one direction only | Battery, phone charger output |
| Alternating Current (AC) | Direction of flow reverses periodically (50 or 60 Hz) | Household outlets, power grid |
Voltage (V, measured in Volts) is the energy given to each unit of charge by a source. It is often described as "electrical pressure" — the push that drives current through a circuit.
Resistance (R, measured in Ohms, symbol Ω) is the opposition to current flow. All conductors have some resistance. Resistivity depends on the material and increases with temperature for most metals.
Resistivity
- Resistivity is a property of the material itself, not the component.
- For most metals, resistance increases with temperature (more collisions as atoms vibrate faster).
- For semiconductors, resistance decreases with temperature.
Use the triangle method: write V on top, I and R on the bottom. Cover what you want to find — what remains shows the operation.
Ohmic vs Non-Ohmic Devices
| Type | V-I graph | Resistance | Example |
|---|---|---|---|
| Ohmic | Straight line through origin | Constant (slope = R) | Resistor, metal wire at constant temperature |
| Non-ohmic | Curved line | Changes with current / temperature | Diode, light bulb filament, thermistor |
In a series circuit, all components are connected in a single loop. There is only one path for current to flow, so the same current passes through every component.
Rₜ = 4 + 8 = 12 Ω · I = 12 / 12 = 1 A
V₁ = 1 × 4 = 4 V · V₂ = 1 × 8 = 8 V · Check: 4 + 8 = 12 V ✓
In a parallel circuit, components are connected across the same two nodes. Each branch receives the full supply voltage. Adding more branches provides more paths for current, so total resistance decreases.
1/Rₜ = 1/8 + 1/12 = 3/24 + 2/24 = 5/24 → Rₜ = 4.8 Ω
I₁ = 24/8 = 3 A · I₂ = 24/12 = 2 A · Iₜ = 5 A
Real circuits combine series and parallel sections. Solve them by simplifying step by step:
- Step 1 — Identify all series sections and all parallel groups.
- Step 2 — Reduce each parallel group to its equivalent resistance using 1/Rₜ = 1/R₁ + 1/R₂ + …
- Step 3 — Add all remaining resistances in series to get the total Rₜ.
- Step 4 — Use V = IR to find the total current from the source.
- Step 5 — Work backward through the circuit to find individual voltages and currents.
Power (P, Watts) is the rate at which energy is transferred or converted. Three equivalent forms — choose based on what you know:
Energy
A magnetic field (symbol B, measured in Tesla, T) surrounds moving charges and current-carrying wires. Magnetic fields exert forces on other moving charges and currents.
Force on a Moving Charge
Force on a Current-Carrying Wire
Right-Hand Rules
- Field around a wire: point thumb in direction of conventional current; fingers curl in the direction of the magnetic field.
- Force on a wire (motor rule): point fingers in the direction of current, curl toward B field; thumb points in the direction of the force.
- The magnetic force is always perpendicular to both the velocity (or current) and the field — it never does work along the direction of motion.
Electromagnets
- A solenoid (coil of wire) creates a uniform magnetic field inside when current flows.
- Increasing current or increasing the number of turns strengthens the field.
- Inserting a ferromagnetic core (e.g. iron) concentrates and greatly amplifies the field.
| Mistake | What to do instead |
|---|---|
| Current splits in series | Current is the same everywhere in a series circuit. Only voltage splits. |
| Voltage splits in parallel | Voltage is the same across every branch in a parallel circuit. Only current splits. |
| Parallel Rₜ bigger than branches | Parallel total resistance is always less than the smallest branch resistance. |
| Using P = I²R in parallel | When branches share the same voltage, use P = V²/R for each branch. |
| Using P = V²/R in series | When components share the same current, use P = I²R for each component. |
| Magnetic force along direction of motion | F = qvB sinθ is always perpendicular to v and B — it changes direction, not speed. |
| Forgetting θ in F = qvB sinθ | If the charge moves parallel to B (θ = 0°), the magnetic force is zero. |