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Electricity — Circuits, Current & Power

Grade 11 Physics  ·  Topic Summary  ·  Emil Oliversen
Contents
  1. Electric Charge & Current
  2. Voltage & Resistance
  3. Ohm's Law Applications
  4. Series Circuits
  5. Parallel Circuits
  6. Mixed Circuits
  7. Power & Energy
  8. Magnetism Basics
  9. Common Mistakes
1 Electric Charge & Current

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).

Current
I = Q / t   (A = C / s)

Conventional vs Electron Flow

DC vs AC

TypeDescriptionExample
Direct Current (DC)Charge flows in one direction onlyBattery, phone charger output
Alternating Current (AC)Direction of flow reverses periodically (50 or 60 Hz)Household outlets, power grid
💡1 Ampere = 1 Coulomb per second. A typical household circuit carries 10–20 A. A lightning bolt can carry 20,000 A for a fraction of a millisecond.
2 Voltage & Resistance

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.

Voltage
V = energy / charge   (Volts = Joules / Coulomb)
Resistance
R in Ohms (Ω)  — opposes current flow
🔑Think of voltage as water pressure, current as flow rate, and resistance as the narrowness of the pipe. Higher pressure drives more flow; a narrower pipe restricts it.

Resistivity

3 Ohm's Law Applications
📐Ohm's Law: V = IR  — the voltage across a component equals the current through it multiplied by its resistance.
Find voltage
V = I × R
Find current
I = V / R
Find resistance
R = V / I

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

TypeV-I graphResistanceExample
OhmicStraight line through originConstant (slope = R)Resistor, metal wire at constant temperature
Non-ohmicCurved lineChanges with current / temperatureDiode, light bulb filament, thermistor
💡For a V-I graph of an ohmic device, the slope = R. Steeper slope = higher resistance.
4 Series Circuits

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.

Current (same)
I is identical everywhere in the loop
Total resistance
Rₜ = R₁ + R₂ + R₃ + …
Voltage divides
Vₜ = V₁ + V₂ + V₃ + …
Voltage ratio
V₁ / V₂ = R₁ / R₂
✏️
Example: 12 V battery, R₁ = 4 Ω, R₂ = 8 Ω in series.
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 series circuit, the largest resistor gets the largest share of the voltage. If one component fails (open circuit), all current stops — the whole circuit goes dead.
5 Parallel Circuits

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.

Voltage (same)
V is identical across every branch
Total resistance
1/Rₜ = 1/R₁ + 1/R₂ + 1/R₃ + …
Two resistors shortcut
Rₜ = (R₁ × R₂) / (R₁ + R₂)
Current divides
Iₜ = I₁ + I₂ + I₃ + …
⚠️Key fact: The total parallel resistance is always less than the smallest individual branch resistance. Adding more branches always lowers Rₜ.
✏️
Example: 24 V, R₁ = 8 Ω, R₂ = 12 Ω in parallel.
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
💡Household wiring is parallel so each appliance gets the full 120 V (or 240 V) and can be switched on/off independently without affecting others.
6 Mixed (Series-Parallel) Circuits

Real circuits combine series and parallel sections. Solve them by simplifying step by step:

🔑Always simplify parallel groups first, then add in series. Draw the simplified circuit at each step to avoid errors.
7 Electrical Power & Energy

Power (P, Watts) is the rate at which energy is transferred or converted. Three equivalent forms — choose based on what you know:

P = VI
Use when voltage and current are both known
P = I²R
Use when current and resistance are known (series circuits)
P = V²/R
Use when voltage and resistance are known (parallel circuits)

Energy

Energy (Joules)
E = P × t = V × I × t
Kilowatt-hour
1 kWh = 3.6 × 10⁶ J
Electricity cost
Cost = (P in kW) × (time in h) × (rate in $/kWh)
💡Electricity bills use kWh, not Joules. A 1500 W heater running for 2 hours uses 3 kWh. At $0.12/kWh that costs $0.36.
8 Magnetism Basics

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

F = qvB sinθ
q = charge (C), v = speed (m/s), B = field (T), θ = angle between v and B

Force on a Current-Carrying Wire

F = BIL sinθ
B = field (T), I = current (A), L = wire length (m), θ = angle between I and B

Right-Hand Rules

Electromagnets

💡If θ = 90° (velocity perpendicular to B), the force is maximum. If θ = 0° (velocity parallel to B), the force is zero. A moving charge parallel to a magnetic field feels nothing.
9 Common Mistakes to Avoid
MistakeWhat to do instead
Current splits in seriesCurrent is the same everywhere in a series circuit. Only voltage splits.
Voltage splits in parallelVoltage is the same across every branch in a parallel circuit. Only current splits.
Parallel Rₜ bigger than branchesParallel total resistance is always less than the smallest branch resistance.
Using P = I²R in parallelWhen branches share the same voltage, use P = V²/R for each branch.
Using P = V²/R in seriesWhen components share the same current, use P = I²R for each component.
Magnetic force along direction of motionF = qvB sinθ is always perpendicular to v and B — it changes direction, not speed.
Forgetting θ in F = qvB sinθIf the charge moves parallel to B (θ = 0°), the magnetic force is zero.