Unformatted text preview: Energy and Power 1 Energy Energy is the capacity of matter to
Energy is conserved.
• It can be neither created nor
The unit of energy is the Joule and is
the same as the unit of work. 2 Power Power = energy per unit time (by
= ∆ 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
p = Δw/Δt = (Δw/Δq)(Δq/Δt) = 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 4 Example Uniform electric field
B 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 =Δq/Δt=2/.5 = 4 A, p=vi=(1)(4)
5 Power and Energy Power is an instantaneous
• Light bulbs rated in watts
Motors rated in Horsepower
(746 watts) Energy is a time average
• Electricity is sold in kilowatthours (7.82 cents per kW-hr in
6 Passive Sign Convention If P > 0,
then LOAD Absorbing Power
(LOAD) If P < 0, then
SOURCE 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
B. 1, 2
C. 2, 3
D. 4, 5
E. 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
Element 3 is a
B. Independent voltage source
C. Dependent current source
depending on current I
D. Dependent voltage source
depending on voltage 0.6I
E. None of the above Which of the following is correct?
B. P1 = -40W
C. P2 = -16W
D. P3 = -9W 17 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?
B. P1 = 5 X 8 W
C. P2 = 2 X 8 W
D. P3 = - 0.6 X 5 X 3 W
E. P4 = - 3 X 5 W 18 Practice Problem Determine Is 19 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. 20 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? 21 ...
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This note was uploaded on 03/22/2008 for the course EE 302 taught by Professor Mccann during the Fall '06 term at University of Texas.
- Fall '06