Power in circuits - Physics 2 AP Study Notes

Electrical Power is the rate of energy transfer in a circuit, measured in watts (W), where 1 watt equals 1 joule per second. Power represents how quickly electrical energy is converted to other forms (heat, light, motion).

Key Equations:

P = IV (Power = Current × Voltage)

This fundamental relationship shows power dissipated when current I flows through a potential difference V.

P = I²R (derived by substituting V = IR)

Useful when resistance and current are known. Shows power is proportional to the square of current—doubling current quadruples power dissipation.

P = V²/R (derived by substituting I = V/R)

Ideal when voltage and resistance are known. Shows power is inversely proportional to resistance for constant voltage.

Energy Transfer: W = Pt (Energy = Power × time)

Measured in joules (J) or kilowatt-hours (kWh) for practical applications. 1 kWh = 3.6 MJ.

Mnemonic: "PIV-R-IVR" - Power-I-V-Relationship: I²R, IV, V²/R

Important Principles:

• Power dissipated in a resistor converts to thermal energy (Joule heating)
• In series circuits: components with higher resistance dissipate more power (P ∝ R when I is constant)
• In parallel circuits: components with lower resistance dissipate more power (P ∝ 1/R when V is constant)
• Conservation of energy: Total power supplied by source equals sum of power dissipated by all components
• Efficiency = (Useful power output / Total power input) × 100%

Cambridge Key Term: "Rate of energy transfer" is the preferred definition over "rate of doing work" in electrical contexts.

Understanding power in circuits explains everyday electrical phenomena and engineering decisions.

Real-World Applications:

Household Appliances: A 2400W electric kettle draws P/V = 2400/230 = 10.4A from mains supply. The high power rating means rapid energy transfer—boiling water quickly. Compare this to a 60W lamp: same voltage, but dramatically less current (0.26A) and slower energy conversion.

Power Transmission: Electricity companies use high voltage transmission (400kV) to minimize power loss. Using P = I²R, reducing current (by increasing voltage for same power) dramatically cuts resistive losses in cables. A 1000MW power station transmitting at 400kV needs only 2500A, but at 40kV would require 25,000A—causing 100× greater heating losses!

Water Flow Analogy:

• Voltage = water pressure (height difference)
• Current = flow rate (liters/second)
• Power = energy delivery rate

A waterfall (high voltage) with modest flow (current) delivers same power as a wide river (high current) with gentle drop (low voltage). Power = pressure × flow rate.

Fuses and Circuit Protection: A 13A fuse in a UK plug protects against excessive power dissipation (P = IV = 13 × 230 = 2990W max). Exceeding this causes the fuse wire to heat, melt, and break the circuit—preventing fires.

LED vs. Incandescent Bulbs: A 10W LED produces same light as a 60W incandescent bulb. Both operate at 230V, but the LED draws much less current (0.043A vs. 0.26A). The incandescent wastes 50W as heat—demonstrating low efficiency (only 17% efficient vs. LED's 60%).

Key Insight: High resistance in transmission lines is problematic because P = I²R means even small currents cause significant heating when current is high.