Master the physics principles you need for Canadian apprenticeship exams and real-world applications
Voltage (V): Electrical potential difference measured in volts. It's the "push" that drives electrons through a circuit.
Current (I): Flow of electrons measured in amperes (amps). It's the "flow" of electricity.
Resistance (R): Opposition to current flow, measured in ohms (Ω). Materials like copper conduct well (low resistance); materials like rubber resist (high resistance).
V = I × R
Voltage equals current multiplied by resistance
P = I × V
P = V² ÷ R
P = I² × R
Power in watts; choose the formula that matches your known values
Series Circuits: Components connected end-to-end. Current is the same through all components. Voltages add up. Total resistance = R₁ + R₂ + R₃
Parallel Circuits: Components connected between the same two points. Voltage is the same across all branches. Currents add up. Total resistance is calculated as: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃
Most industrial and commercial systems use three-phase power, which provides more efficiency than single-phase. Three-phase power delivers constant power (no dips like single-phase) and uses smaller conductors for the same power level.
P = √3 × V × I × Power Factor
√3 ≈ 1.732; power factor typically 0.8-1.0 for industrial loads
Problem: A 120V circuit has a total resistance of 24 ohms. What is the current?
Problem: A motor draws 8 amps at 240V. How many watts is it consuming?
Problem: Three resistors of 12Ω, 12Ω, and 6Ω are connected in parallel. What is the total resistance?
Every magnet has a magnetic field—an invisible region where magnetic forces act. When a conductor moves through a magnetic field or a magnetic field changes near a conductor, an electrical current is induced in that conductor. This is electromagnetic induction, discovered by Faraday.
The strength of an induced current depends on: the strength of the magnetic field, the speed of change, and the number of wire turns in a coil.
Transformers use electromagnetic induction to change voltage levels. A primary coil (input) creates a changing magnetic field, which induces a voltage in a secondary coil (output). The voltage ratio depends on the turns ratio.
V_primary / V_secondary = N_primary / N_secondary
I_primary / I_secondary = N_secondary / N_primary
As voltage steps down, current steps up (power remains constant, ignoring losses)
Direct Current (DC): Electrons flow in one direction. Used in batteries, electronics, some industrial equipment. Voltage is constant.
Alternating Current (AC): Electrons reverse direction periodically (50-60 cycles per second = 50-60 Hz). Standard for power grids in Canada (60 Hz). AC is easier to transform to different voltages, so it's ideal for long-distance transmission.
An electric motor reverses the generator principle. A current-carrying wire in a magnetic field experiences a force (left-hand rule for motors). By switching the current direction using a commutator (DC) or by using AC's alternating nature, the wire continuously rotates.
Problem: A transformer has 2,400 turns on the primary coil and 200 turns on the secondary coil. The primary voltage is 4,800V. What is the secondary voltage?
Problem: A transformer steps down from 480V to 120V. The primary current is 2 amps. What is the secondary current?
Problem: Canadian power is 60 Hz AC. What is the period (time for one complete cycle)?
Pascal's Law states: "Pressure applied to a fluid is transmitted equally in all directions." This principle allows a small force on a small area to create a large force on a large area—the basis of hydraulic lifting and pressing.
P = F / A
Pressure (Pa or psi) = Force (N or lbs) ÷ Area (m² or in²)
In a hydraulic system, the same pressure acts throughout the fluid. Therefore, if you have different-sized pistons/cylinders, you can amplify force:
F = P × A
Mechanical Advantage = A_load / A_effort
Larger output area provides greater force multiplication
Flow rate tells you how much fluid moves through the system per unit time. It determines speed of operation and power.
Q = V / t
Q = A × v
Flow rate (L/min or gal/min) = Volume / Time, or Area × Velocity
In any fluid system, the weight of the fluid column creates pressure at the bottom. This is important for pump selection and system design.
P = ρ × g × h
Pressure = Density × Gravity × Height. Or: 1 meter of water ≈ 9.81 kPa; 1 foot ≈ 0.433 psi
Problem: A hydraulic system has a pressure of 2,000 psi. The input piston is 1 in² and the output cylinder is 50 in². What force is exerted on the load?
Problem: A hydraulic cylinder has a piston area of 20 cm². A force of 40,000 N is applied. What is the pressure in the cylinder?
Problem: A pump delivers 100 liters of fluid per minute into a hydraulic system. If the system line has a cross-sectional area of 5 cm², what is the fluid velocity?
Sensible Heat: Heat that causes a temperature change. When you add sensible heat to water at 20°C, its temperature increases. You can measure this temperature change with a thermometer.
Latent Heat: Heat that causes a phase change (solid → liquid → gas) without changing temperature. When water boils at 100°C, adding more heat doesn't increase temperature; it converts liquid to steam. This "hidden" heat is critical in refrigeration cycles.
Different materials require different amounts of heat to raise their temperature by one degree. This is specific heat capacity.
Q = m × c × ΔT
Heat (J or BTU) = Mass (kg or lbs) × Specific Heat (J/kg·°C or BTU/lb·°F) × Temperature Change
Conduction: Direct transfer of heat through a material. Example: a metal rod heated at one end; heat travels along the rod by molecular vibration.
Convection: Heat transfer through a moving fluid (liquid or gas). Example: warm air rising from a heater spreads heat around a room.
Radiation: Heat transfer via electromagnetic waves. Example: standing near a campfire or feeling the sun's warmth. No medium needed.
British Thermal Units (BTU) measure heat in imperial units; kilowatts (kW) in metric. 1 BTU ≈ 1.055 kJ; 1 kW = 3.412 BTU/h
Heating Capacity (BTU/h) = Power (kW) × 3,412
Power (kW) = BTU/h ÷ 3,412
HVAC and heating systems often use BTU; electrical systems use kW
A refrigerant circulates through four stages: (1) Evaporation (cold side—absorbs heat from the space), (2) Compression (compressor pressurizes the gas), (3) Condensation (hot side—rejects heat to outside), (4) Expansion (pressure drops before returning to evaporator). This cycle continuously moves heat from cold to hot (with energy input).
Problem: You need to heat 50 kg of water from 20°C to 80°C. Specific heat of water = 4,186 J/(kg·°C). How much heat energy is required?
Problem: An air conditioning unit is rated at 60,000 BTU/h. What is its cooling capacity in kilowatts?
Problem: A 2 kW electric heater runs for 3 hours. How much heat (in BTU) is produced?
Newton's Second Law: Force causes acceleration. The more force applied, the greater the acceleration (if mass is constant). A heavier object requires more force to accelerate at the same rate.
F = m × a
Force (N) = Mass (kg) × Acceleration (m/s²); 1 Newton = 1 kg·m/s²
Torque is a twisting or turning force. It depends on both the force applied and the distance from the pivot point. A wrench is long to provide leverage—the same muscle force creates more torque with a longer wrench.
τ = F × d
Torque (N·m or ft·lbs) = Force (N or lbs) × Perpendicular Distance from Pivot (m or ft)
Mechanical Advantage (MA) is the ratio of output force to input force. It tells you how much the machine multiplies your effort.
Lever (Class 1, 2, 3): A rigid bar pivoting on a fulcrum. MA = distance from effort to fulcrum / distance from load to fulcrum
Pulley: A wheel with a rope. Fixed pulleys change direction (MA = 1); movable pulleys multiply force (MA = 2 or more depending on rope arrangement).
Gears: Interlocking wheels with teeth. Gear ratio = Number of teeth on driven gear / Number of teeth on driving gear. Increased teeth ratio increases torque but decreases speed.
MA = Output Force / Input Force
MA = Distance Input Moves / Distance Output Moves
Rule: You gain force but lose distance (or vice versa)
When lifting loads with slings, cables, or equipment, calculate the safe working load (SWL) based on sling angle, number of slings, and material strength. The angle of the sling affects the vertical component of force and the load on each sling.
Tension = Load / (2 × cos(θ))
Where θ is the angle from vertical; as angle increases, tension increases; vertical lift is most efficient (θ = 0°)
Problem: An 800 kg forklift is accelerating at 0.5 m/s². What force is the engine producing?
Problem: A worker applies 50 N of force at the end of a 0.3 m wrench. What torque is applied to a bolt?
Problem: A crowbar has the fulcrum 0.1 m from the load and the effort force applied 0.6 m from the fulcrum. A worker applies 200 N. What is the output force?
Flow rate (Q) is the volume of fluid moving per unit time. Velocity (v) is how fast the fluid travels. These are related by the pipe's cross-sectional area.
Q = A × v
v = Q / A
Flow rate (m³/s or L/s) = Area (m²) × Velocity (m/s)
In a closed pipe, the mass of fluid flowing is constant. If the pipe narrows (smaller area), the fluid speeds up. If the pipe widens, the fluid slows down. This is critical for understanding velocity and pressure changes.
Q₁ = Q₂ → A₁ × v₁ = A₂ × v₂
If area decreases, velocity increases (and vice versa)
For a flowing fluid, total energy is conserved. As the fluid speeds up (high velocity), pressure decreases, and vice versa. This explains why water flows faster in a narrower pipe and why a moving stream of air has lower pressure (demonstrating a vacuum effect).
P + ½ρv² + ρgh = Constant
Static pressure + dynamic pressure + hydrostatic pressure = constant
Friction between the fluid and pipe walls causes pressure to drop along the pipe. Larger pipes and slower flow reduce pressure drop. This affects pump sizing and efficiency.
Pump head is the height of fluid column a pump can lift against gravity. Total pump head includes static head (vertical distance) plus dynamic head (to overcome friction and create flow).
Static Pressure: Pressure due to the fluid's weight and confinement (not moving).
Dynamic Pressure: Pressure due to the fluid's motion. ½ρv²
Total Pressure: Static + Dynamic
Problem: Water flows through a pipe with a cross-sectional area of 0.05 m². The velocity is 2 m/s. What is the flow rate?
Problem: Water enters a pipe at point 1 with area 0.1 m² and velocity 1 m/s. At point 2, the pipe narrows to 0.05 m². What is the velocity at point 2?
Problem: Air flows through a duct at 10 m/s. The density of air is 1.2 kg/m³. What is the dynamic pressure?
Tensile Strength: The maximum pulling (tensile) force a material can withstand before breaking. Measured in megapascals (MPa) or psi.
Yield Point: The stress level at which a material starts to permanently deform. Below the yield point, the material springs back; above it, permanent damage occurs.
Steel typically has higher tensile strength than aluminum. Cast iron is strong in compression but weak in tension.
Hardness measures resistance to penetration and scratching. Common scales: Rockwell (HRC for hardened steel), Brinell (HB), Mohs (for minerals). Hardness doesn't always correlate with tensile strength; a hard material can be brittle.
Most materials expand when heated and contract when cooled. The coefficient of thermal expansion varies by material. This is why concrete joints and metal expansion loops are installed—to allow for movement without cracking or buckling.
ΔL = L₀ × α × ΔT
Change in length = Original length × Coefficient of thermal expansion × Temperature change
Density is mass per unit volume. It determines how heavy a material is for its size. Used for load calculations, material selection, and understanding buoyancy.
ρ = m / V
Density (kg/m³ or g/cm³) = Mass (kg) / Volume (m³)
Young's modulus measures how much a material resists deformation under stress. High modulus = stiff material (doesn't flex easily). Steel has higher modulus than aluminum.
Steel: High tensile strength (~400-1000 MPa), good hardness, moderate density (7,850 kg/m³), coefficient of thermal expansion ~12 μm/(m·°C)
Aluminum: Lower tensile strength (~70-400 MPa), lower density (2,700 kg/m³), higher thermal expansion (~23 μm/(m·°C))
Copper: Moderate tensile strength (~200-400 MPa), excellent thermal conductivity, density 8,960 kg/m³
Problem: A 10-meter steel beam is installed at 0°C. It will be exposed to temperatures up to 40°C. How much will it expand? (Coefficient of thermal expansion for steel ≈ 12 × 10⁻⁶ /°C)
Problem: A steel plate has a mass of 50 kg and a volume of 0.00636 m³. What is its density?
Problem: Compare the weight of a 1 m³ block of steel (density 7,850 kg/m³) versus aluminum (density 2,700 kg/m³).
Work is done when a force causes displacement. If you push with force but nothing moves, no work is done (even though you might be tired!). Work depends on the force component in the direction of motion.
W = F × d × cos(θ)
Work (J or ft·lbs) = Force × Distance × Cosine of angle between force and motion
Kinetic Energy: Energy of motion. A faster-moving object has more kinetic energy. Doubling speed quadruples kinetic energy (because of the v² term).
Potential Energy: Energy due to position. A raised weight has potential energy. Higher elevation = more potential energy.
KE = ½ × m × v²
Kinetic Energy (J) = Half mass × Velocity squared
PE = m × g × h
Potential Energy (J) = Mass × Gravity (9.81 m/s²) × Height
Power is the rate of doing work or transferring energy. A motor that lifts a load quickly is more powerful than one that does it slowly. Power is measured in watts (W), kilowatts (kW), or horsepower (hp).
P = W / t
P = F × v
Power (W) = Work (J) / Time (s), or Force × Velocity
Energy can convert between forms: electrical → mechanical (motor), mechanical → thermal (friction), thermal → electrical (generator), etc. The total energy is conserved, but some is "lost" as waste heat.
No machine is 100% efficient. Some energy is always lost to friction, heat, and other factors. Efficiency is the ratio of useful output to total input.
Efficiency (%) = (Useful Output / Total Input) × 100%
A typical electric motor is 85-95% efficient; a hydraulic pump is 70-90% efficient
Problem: A crane lifts a 5,000 N load vertically 20 meters. How much work is done?
Problem: A pump does 100,000 J of work in 50 seconds. What is its power output?
Problem: A 1,500 kg vehicle is traveling at 20 m/s. What is its kinetic energy?