7.1 Power, Work & Energy Concepts

7.1 Power, Work & Energy Concepts

Quick Answer: Energy is the capacity to do work; both are measured in joules (J). Power is how fast energy is transferred or converted — measured in watts (W), where 1 W = 1 J/s. In DC circuits, instantaneous electrical power into a load is P = VI. Remember: energy = power × time (W = Pt in consistent SI units).

CAAS SAR-66 Module 3 topic 3.8 Power sits after resistance (3.7) and before capacitance (3.9). You already know voltage, current, and resistance from topics 3.3 and 3.6–3.7. Power answers the maintenance question those quantities alone do not: how hard is this circuit working, and how much heat or mechanical output should I expect?

Work: Force Through a Distance

In mechanics, work done by a constant force in the direction of motion is:

Work = force × distance

W = F × d

1 joule = 1 newton·metre (N·m). If you push with 10 N through 2 m (in the force direction), work = 20 J.

Worked example 1 — mechanical work. A technician applies an average 50 N force while sliding a tool chest 3.0 m along a hangar floor (force aligned with motion). Work = 50 × 3.0 = 150 J.

If the force is perpendicular to the displacement, that force component does no work. Module 3 uses the aligned case for definitions; the exam cares that work and energy share the joule.

Energy: Capacity to Do Work

Energy is the capacity to do work. When a system does 150 J of work, it transfers or converts 150 J of energy. Units match: both use J.

Energy is never “created from nothing” in Module 3 reasoning — it transforms. Chemical energy in a battery becomes electrical energy in the circuit, then thermal energy in a resistor or mechanical energy in a motor.

Kinetic energy (energy of motion)

Kinetic energy (KE) depends on mass and speed:

KE = ½ m v²

Worked example 2 — kinetic energy. A 2.0 kg mass moves at 3.0 m/s.

KE = ½ × 2.0 × (3.0)² = 1.0 × 9.0 = 9.0 J.

Double the speed → four times the kinetic energy, because of v². That squared dependence is a frequent trap on calculation stems.

Potential energy (energy of position or stored state)

Potential energy (PE) is stored energy associated with position or configuration. Common Module 3–relevant forms:

Gravitational PE (near Earth, constant g):

PE = m g h

Worked example 3 — gravitational PE. Raise a 5.0 kg component by 2.0 m (g ≈ 9.8 m/s²).

PE ≈ 5.0 × 9.8 × 2.0 = 98 J.

That 98 J came from the work you did lifting it. If the part falls freely (idealised), PE converts toward KE.

Electrical perspective: A charge q moved through a potential difference V gains or loses electrical potential energy qV (joules when q is in coulombs and V in volts). A battery “stores” chemical energy that the circuit converts as charge flows through voltage drops.

Power: Rate of Doing Work / Transferring Energy

Power is work done (or energy transferred) per unit time:

P = W / t

Equivalently, energy = power × time:

W = P × t

Larger units you will see:

• 1 kW = 1 000 W
• 1 MJ = 10⁶ J
• In industry, energy is often quoted in kilowatt-hours (kWh): 1 kWh = 1 000 W × 3 600 s = 3.6 × 10⁶ J = 3.6 MJ

Module 3 prefers SI (W, J, s) for exam arithmetic, but recognising that a watt is a rate prevents mixing energy and power on stems.

Worked example 4 — power from work and time. A hoist does 2 400 J of useful work in 8.0 s.

P = 2 400 / 8.0 = 300 W.

Worked example 5 — energy from power and time. A 60 W lamp runs for 5.0 minutes (300 s).

Energy = P t = 60 × 300 = 18 000 J = 18 kJ.

If the stem gives minutes or hours, convert to seconds before multiplying, or carefully use hours only with kW·h.

Electrical Power: P = VI

In a DC circuit, the electrical power delivered to a two-terminal load is:

P = V I

Why it works: Voltage is energy per coulomb; current is coulombs per second. Product is joules per second = watts.

Worked example 6 — bus load. A heater on a 28 V aircraft DC bus draws 5.0 A.

P = 28 × 5.0 = 140 W.

Every second, about 140 J of electrical energy converts mainly to heat in the heater element.

Worked example 7 — rearrange for current. A 12 V landing-light circuit dissipates 48 W at the lamp (idealised).

I = P / V = 48 / 12 = 4.0 A.

Worked example 8 — rearrange for voltage. A resistor dissipates 18 W at 3.0 A.

V = P / I = 18 / 3.0 = 6.0 V across that resistor.

Link to Ohm’s law (preview of §7.2)

For a pure resistance with V = IR:

• P = I²R (substitute V = IR into P = VI)
• P = V²/R (substitute I = V/R into P = VI)

All three forms describe the same instantaneous dissipation when Ohm’s law holds. Choose the form that matches the known quantities.

Work, Energy, and Power Triangle

Keep this mental map for Module 3:

1. Work / energy → how much (joules).
2. Power → how fast (watts = joules per second).
3. Time → the bridge: W = P t and P = W / t.

Conservation framing for technicians: Energy leaving the electrical circuit as heat in a resistor, light from a lamp, or shaft work from a motor equals the electrical energy delivered (∫ P dt, or P t if power is constant). Losses in wiring are still energy — they just appear as unwanted I²R heating of conductors (developed fully in §7.2).

Aircraft and Training Context

Worked example 9 — constant power energy. A 100 W avionics heater (training figure) runs for 10 minutes at rated power.

Energy = 100 W × 600 s = 60 000 J = 60 kJ.

Worked example 10 — compare rates. Device A transfers 500 J in 2 s → P = 250 W. Device B transfers 500 J in 10 s → P = 50 W. Same energy, different power — different thermal and supply stress.

Exam Pitfalls to Avoid

• Calling joules “power” or watts “energy”.
• Forgetting v² in kinetic energy.
• Using minutes in W = P t without converting.
• Mixing peak and continuous ratings (Module 3 starts with steady DC P = VI).

Master the SI definitions, KE and PE ideas, P = W/t, and P = VI. Section 7.2 then drills dissipation formulas, resistor heating, and conductor I²R losses that CAAS stems favour.