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WORK, ENERGY AND POWER • • • • • • • • • • • • Work – energy spent to overcome a restraint to achieve a physical change Energy is the ability to do work Energy and work have the same SI units – Joules (J) Power – rate at which energy is expended (Joules/sec) Unit of power = watt = Joules per second = Js-1 Power (P) = Work (W)/Time (t); W = Pt When electrical current flows through a resistance, electrical energy is converted to heat energy at a rate that depends on the voltage across the resistance and the value of current through it, i.e. Power (P) = Voltage (V) × Current (I) (watts) P = V2/R = I2R (watts) Power ‘delivered’ to a resistance = power dissipated in resistance A kilowatt-hour (kWh) is the total energy delivered or consumed in one hour, and is used in industry kWh = (P in kW) × (t in hours) 2. Power and Resistors 1 WORK, ENERGY AND POWER EXAMPLES • A 12V DC power source is connected to a 500Ω resistor that has a tolerance of ±5%. What is the maximum and minimum power that can be dissipated in the resistance? • Electrical energy costs £0.12/kWh. For how long could a 900W oven be operated without costing more than 36p? 2. Power and Resistors 2 POWER RATING OF RESISTORS • • • • If the power rating of a resistor is too small for a particular application, then the resistor will not be able to dissipate heat at a rate rapid enough to prevent destructive temperature build up Resistors that are physically large in size have a greater surface area, so they dissipate heat faster Resistors are used to control the flow of current in part of a circuit Question: A 200Ω resistor has a 2W power rating. What is the maximum current that can flow in the resistor without exceeding the power rating? 2. Power and Resistors 3 TEMPERATURE CHARACTERISTICS OF RESISTORS • • Resistors are constructed from metal alloys (hybrids of more than one element), metal oxide (metals containing oxygen atoms) films or carbon composites. Resistance values of resistors are dependent on temperature. Rθ = R0 (1 + aθ ) • • • • • Rθ is the resistance at temperature θ R0 is the resistance at 0°C a is the temperature coefficient θ is the temperature in °C Example What is the value of a 6.8kΩ resistor at 95°C if the temperature coefficient is 1.2e-3? • Example If a resistor with a temperature coefficient of 1.5e-3 has a value of 10Ω at 20°C, what is its resistance at 80°C? 2. Power and Resistors 4 RESISTOR COLOUR CODES • • • • • • • • • • • • • 0 1 2 3 4 5 6 7 8 9 5% 10% 20% • Yellow; violet; orange; silver = 47×103Ω ±10% Brown,black,red? Blue,grey,black,gold? • • Black Brown Red Orange Yellow Green Blue Violet Grey White Gold Silver None 1st 2nd 3rd Tolerance 2. Power and Resistors 5 STANDARD RESISTOR VALUES • • • • • • • • • • • • • • Resistors are available in a number of standard ranges These ranges, or series, are set up by the Electronics Industries Association (EIA) They are: E3, E6, E12, E24, E48, E96, E192 The number after the ‘E’ denotes the number of values the series contains per decade (every factor of 10) Resistors with a tighter tolerance can have more values in the series that won't overlap one another E3: 50% tolerance E6: 20% tolerance E12: 10% tolerance E24: 5% tolerance E48: 2% tolerance E96: 1% tolerance E192: less than 1% tolerance http://www.hardwarebook.info/EIA_resistors Question: A 9V battery is connected to an E12 resistor of 560Ω. What is the range of possible current flow in such a circuit? 2. Power and Resistors 6 STANDARD PREFIXES AND SYMBOLS • • • • • • • Pico (p) ×10-12 e.g. 1.8p Nano (n) ×10-9 e.g. 4.7n Micro (µ) ×10-6 e.g. 0.1µ Milli (m) ×10-3 e.g. 10m Kilo (k) ×103 e.g. 9.8k Mega (M) ×106 e.g. 1M Giga (G) ×109 e.g. 1.8G 2. Power and Resistors 7 CONDUCTANCE • • • • • • • Conductance is the reciprocal of resistance Conductance is the ability of a material to pass electrons The higher the resistance, the lower the conductance Symbol of Conductance is G Unit of conductance is the Siemen (S) G = 1/R Siemens What are the resistance and conductance ranges of a 75kΩ ± 10% resistor? 2. Power and Resistors 8