and Energy Power
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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.
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Power
Power = energy per unit time (by definition) = Dw/Dt 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.
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Relationship: power, voltage and current
p = w/t = (w/q)(q/t) = vi
where p = power in Watts v = voltage in Volts i = current in Amperes q = charge in Coulombs
Check:
p (joules/second) = v (joules/coulomb) x i
(coulombs/sec.)
p = vi
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Uniform electric field B
Example
We move 2 coulombs from A to B in 0.5 seconds and get 1 Volt A
What are the current and power? Answer: 4 A and 4 W
v = 1 Volt, i =q/t=2/.5 = 4 A, p=vi=(1)(4) W
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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 kW-hr in Austin)
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Passive Sign Convention
If P > 0, then LOAD
If P < 0, then SOURCE
Absorbing Power (LOAD)
Supplying Power (SOURCE)
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Total Power in a circuit is always conserved.
Power delivered = Power consumed
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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. 1, 2
B. 2, 3 C. 4, 5
D. 2, 4
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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
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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
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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
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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.
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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.
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Independent Sources
Voltage Source
Current Source
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Dependent Sources
Dependent Voltage Source
Dependent Current Source
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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. P1 = 5 X 8 W B. P2 = 2 X 8 W
C. P3 = - 0.6 X 5 X 3 W
D. P4 = - 3 X 5 W
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Practice Problem
Determine Is
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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.
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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?
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