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Section 3.8

Power

Power, work and energy (kinetic and potential); dissipation of power by a resistor; the power formula and the maximum power transfer theorem.

Notes

Power, summary notes

Main ideas
  • Power is the rate of doing electrical work, measured in watts. P = V × I.
  • Substituting Ohm's law gives two more forms: P = I²R and P = V²/R. Choose the one using the two quantities you are given.
  • Energy is power multiplied by time: W = P × t, in joules or kilowatt-hours.
  • Maximum power is transferred to a load when the load resistance equals the source's internal resistance.
  • ⚠ Exam trap: pick the power formula that matches the given quantities. Converting unnecessarily through Ohm's law first invites arithmetic errors.
Key formulas
Power
P = V × I = I²R = V² / R (watts)
Energy
W = P × t (joules)
Max power transfer
R_load = R_source
Solved examples

  1. A 28 V landing lamp draws 5 A. What power does it dissipate?

    P = V × I = 28 × 5 = 140 W.

  2. A 4 Ω resistor carries 3 A. Find the power dissipated.

    Current and resistance are given, so use P = I²R = 3² × 4 = 9 × 4 = 36 W.

Mind map

Power concept map

Power

Quiz

Power quiz

Power, quiz

Ref 3.8Pass 75%

  1. 1. The power triangle shown has a true power of 800 W and an apparent power of 1000 VA. The power factor is:

    P = 800 WQ (reactive)S = 1000 VAφ
    0.8
    1.25
    0.6

  2. 2. A current of 3 A flows through a 4 Ω resistor. The power dissipated is:

    36 W
    12 W
    48 W

  3. 3. A 12 V supply is applied across a 6 Ω resistor. The power dissipated is:

    24 W
    72 W
    2 W

  4. 4. A charge of 20 coulombs passes a point in 10 seconds. The current is:

    2 A
    200 A
    0.5 A

  5. 5. A 28 V lamp draws 5 A. The power dissipated is:

    140 W
    5.6 W
    33 W

  6. 6. A 4 Ω resistor carries 3 A. The power dissipated is:

    36 W
    12 W
    48 W

  7. 7. Maximum power is transferred to a load when:

    Load resistance equals source internal resistance
    Load resistance is as low as possible
    Load resistance is as high as possible

  8. 8. A 24 V supply across a 12 Ω resistor dissipates:

    48 W
    2 W
    288 W

  9. 9. Electrical energy is the product of:

    Power and time
    Voltage and current
    Current and resistance

  10. 10. If the current through a fixed resistor is doubled, the power dissipated:

    Quadruples
    Doubles
    Halves

  11. 11. The unit of electrical power is the:

    Watt
    Joule
    Volt-ampere reactive

  12. 12. A 100 W load runs for 3 hours. The energy consumed is:

    0.3 kWh
    300 kWh
    33 kWh

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