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Unformatted text preview: Energy and Power 1 Energy Energy is the capacity of matter to perform work Energy is conserved. It can be neither created nor destroyed. The unit of energy is the Joule and is the same as the unit of work. 2 Power Power = energy per unit time (by definition) = w/ t where w = the energy in joules t = the time in seconds The unit of power is the Watt named after James Watt (1736 1819) an English inventor who developed the steam engine. 3 Relationship: power, voltage and current
p = w/ t = (w/ q)(q/ t) = vi
wher e p = power i n Watts v = vol tage i n Vol ts i = cur r ent i n Amper es q = char ge i n Coul ombs Check:
p (joul es/ second) = v (joul es/ coul omb) x i (coul ombs/ sec.) p = vi 4 Example
Uni for m el ectr i c fi el d B We move 2 coul ombs fr om A to B i n 0.5 seconds and get 1 Vol t A What ar e the cur r ent and power ? Answer : 4 A and 4 W v = 1 Vol t, i =q/ t=2/ .5 = 4 A, p=vi =(1)(4) W
5 Power and Energy Power is an instantaneous quantity Light bulbs rated in watts Motors rated in Horsepower (746 watts) Energy is a time average quantity. Electricity is sold in kilowatthours (7.82 cents per kWhr in Austin) 6 Passive Sign Convention If P > 0, then LOAD If P < 0, then SOURCE Absorbing Power (LOAD) Supplying Power (SOURCE) 7 Total Power in a circuit is always conserved.
Power delivered = Power consumed 8 Practice Problem If P1 = -100 W, P2 = 60W, P3 = -55W, P4 = 250W, calculate the power received or delivered by element 5. The following elements are loads in the circuit: A. B. C. D. 1, 2 2, 3 4, 5 2, 4 9 Practice Problem
To move charge q from point A to point B requires -30J. Find the voltage drop vab if (a) q=2C, (b) q=-6 C (a) Vab = w/q = -30/2 = 15 V (b) Vab = w/q = -30/-6 = 5 10 Practice Problem A stove element draws 15 A when connected to a 120 V line. How long does it take to consume 30 kJ? p = v i = 15 x 120 = 1800 watts; w = p x t therefore, t = w/p = (30x103)/1800 = 16.7 seconds 11 The Ideal Basic Circuit Element It has only two terminals It is described mathematically in terms of current and voltage It cannot be subdivided into other circuit elements 12 Active and Passive Elements
Active Element: Capable of generating energy. Eg. Batteries, power supplies Passive Element: Incapable of generating energy Eg. Resistors, capacitors, and inductors. 13 Active Elements
Voltage or Current Sources: Can deliver power to the circuit. Ideal Independent Source: Provides a specified voltage or current, independent of other circuit elements. Ideal Dependent Source: Source quantity is controlled by another voltage or current.
14 Independent Sources Voltage Source Current Source 15 Dependent Sources Dependent Voltage Source Dependent Current Source 16 Practice Problem
Calculate the power absorbed or supplied by each component in the circuit below. Power is conserved
Which of the following statements is true below? A. B. C. D. P1 = 5 X 8 W P2 = 2 X 8 W P3 = 0.6 X 5 X 3 W P4 = 3 X 5 W 17 Practice Problem Determine Is 18 Practice Problem
A 1.2 kW toaster takes roughly 4 minutes to heat four slices of bread. Find the cost of operating the toaster once a day for 1 month (30 days). Assume energy costs 9 cents/kWh. 19 Practice Problem
A battery may be rated in ampere-hours (Ah). A certain battery is rated at 160 Ah. What is the maximum current it can supply for 40 h? How many days will it last if it is discharged at 1mA? 20 ...
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- Fall '06