Power AIM: To be able to use the power equations PRIOR KNOWLEDGE: Know about resistance and the resistor equation, understand voltage and current www.pfnicholls.com

Power – Basic Theory THEORY: POWER = VOLTAGE x CURRENT P = V x I Power tells us how much energy is transferred each second. It lets us know how hot a resistor will get or how long it will take to boil the kettle. THEORY: POWER = VOLTAGE x CURRENT P = V x I Power is measured in Watts (W), milliwatts (mW) or kilowatts (kW) Power is also defined using a different equation. In Physics we learn that Power = Energy transferred per second. A 60W bulb will transfer 60Joules of electrical energy to heat and light energy each second. A 1kW bulb transfers 1000J each second and is brighter!

LEARN these different forms of the power equation Examples Rearranging the Power equations gives: P = V x I V = P  I I = P  V A current of 2A flows through a 12v bulb. What is the power? P = V x I P = 12 x 2 P = 24W How much current does a 60W mains bulb take (V = 240V)? I = P  V I = 60 / 240 I = 0.25A = 250mA A 60mW LED takes a current of 20mA, what is the voltage? V = P  I V = 60 x 10-3 / 20 x 10-3 V = 0.06 / 0.02 = 3V LEARN these different forms of the power equation

Power – Full Theory The fundamental theory is: Power = Energy transferred / time taken (P = E / t) But in electronics we always use: Power = Voltage x Current (P = V x I) This is because we also know: Voltage = Energy /Charge (V = E / Q) Current = Charge / time (I = Q / t) Combining all these equations: P = V x I = (E / Q) x (Q / t) = (E x Q) / (Q x t) = E / t

Power – Alternative Equations Resistors get hot because they dissipate power. We need to be able to use the power equation and resistor equations together. P = V x I and V = I x R Equation 1: P = V x I = (I x R) x I = I x I x R = I2 R P = I2 R Equation 2: P = V x I = V x (V / R) = V x V / R = V2 / R P = V2 / R P = I2 R P = V2 / R LEARN these different forms of the power equation

Examples Remember: P = I2 R P = V2 / R P = V x I V = I x R A current of 3A flows through a 10Ω resistor. What is the power? P = I2 R P = 3 x 3 x 10 P = 90W A 4Ω resistor dissipates 100W. What is the voltage? P = V2 / R 100 = V2 / 4 V2 = 400 V = 20V What is the current in the previous example? P = I2 R 100 = I2 x 4 I2 = 100 / 4 = 25 I = 5A

Power and Resistors Resistors get hot. If they get too hot they stop working. All resistors have a maximum power rating. The voltage and current should be such that the maximum power is not exceeded. The maximum power rating of the small carbon or metal film resistors used in circuit building is determined by their size but is usually ¼W (250mW) or ½W (500mW). Power resistors have the power marked on the body using text e.g. 5W or 10W. E.g. A current of 20mA flows through a current limiting resistor which has a potential difference of 3V. What is the minimum power rating? P = V x I = 3 x 20 x10-3 = 60mW therefore a ¼W resistor will be suitable. A power rating of ⅛W would also be okay.

Power and Domestic Electricity In the domestic context, the power equation is used to calculate suitable ratings for fuses or circuit breakers. The rating of the fuse or circuit breaker must be the lowest sensible value that is above the maximum current required. For domestic plugs, fuses of 3A, 5A and 13A ratings are available For domestic circuits, circuit breakers are either 5A, 10A or 30A For electronic devices, fuses can be 250mA, 500mA, 1A etc In cars, fuses used are 5A, 10A, 20A, 30A etc

Power and Domestic Electricity Examples: What fuse should be used with a 2 kW kettle if the mains voltage is 230 V? I = P ÷ V → I = 8.7A  Use 13A fuse An electric shower is on a 30 A circuit breaker. What is the maximum power of the shower? P = V x I  Pmax = 230 x 30 = 6.9kW A pair of 12V car headlights connected in parallel each have a power rating of 48W. What size fuse should be used? I = P ÷ V → I = 48 ÷ 12 = 4A each. Itotal = 8A  Use a 10A fuse What fuse should be used with a 60W desk lamp? I = P ÷ V → I = 60 ÷ 230 = 0.26A  Use 3A fuse

Summary In Physics: Power = Energy transferred ÷ time taken P = E/t In electronics Power = Voltage x Current P = VI When energy is dissipated in a resistor, such as a heating element, a light bulb filament or a standard resistor, we can also use Power = Current2 x Resistance P = I2R Power = Voltage2 ÷ Resistance P = V2/R The current rating of a fuse or circuit breaker must be greater than the maximum current that will flow in the circuit under normal circumstances i.e. in the absence of a fault.

Questions A current of 2A flows through a 12 resistor. What power is dissipated in the resistor? An electric toaster works from the 230V mains supply. If it has a power rating of 690W, what current flows? What is the resistance of the heating element in Question 2? A torch battery provides 6V and the bulb takes a current of 60mA. What power is the torch bulb? A computer has a power rating of 480W and runs off the mains supply, what is the most appropriate fuse to use?

Answers P = I2R  P = 22 x 12 P = 48W I = P / V  I = 690 / 230 I = 3A R = V / I  R = 230 / 3 R = 77 P = I x V  P = 60 x 10-3 x 6 P = 0.36W I = P / V  I = 480 / 230 I = 2.1A Use a 3A fuse