Transcript Ohms Law & Power

Today’s Agenda
Potentiometers
Ohm’s Law Continued
Power & Energy
Review from Last Week
• How is voltage related to charge and
energy?
• What is the formula for resistance?
• What is Ohm’s Law?
• What does it mean?
•
•
•
•
V = E/Q
R = ρ(L/A)
V = IR
Voltage, resistance, and current are
related linearly
–
–
–
V = IR
R = V/I
I = V/R
Potentiometers
• A potentiometer is a variable resistor
• The total resistance is fixed between terminals
A and B
A
• A portion of the resistance
is between A and C
C
• The remainder is between
B and C
B
• C can be physically moved between A and B
2 Basic Ways to Use
Potentiometers
• As a variable resistor:
– The center tap (C) is
connected to one end
(B)
– The total resistance is
only from A to C
• As a voltage divider
(to be covered in a later
lecture)
A
B/C
In-Class Activity
If you have a 1k Ω potentiometer and the
center tap, C, is set ¼ of the way between
A and B (closer to A),
• What is the resistance between A and C
and between B and C?
• What is the resistance R if the
potentiometer is connected as below
(assume C has not been moved):
R
A
B/C
• The resistance between A and C is ¼ of
the total resistance, i.e. 250 Ω
• The resistance between B and C is ¾ of
the total resistance, i.e. 750 Ω
• The resistance R is 250 Ω
Relationship between Current and
Voltage
• Current through a FIXED resistance
– Increases when the voltage increases
– Decreases when the voltage decreases
• The current changes as a result of the change
in voltage!
+
+
_
_
What is the value of the resistance?
• If R is fixed and I = V/R, then
– Current and voltage are directly proportional
so current increases when voltage increases
•
•
•
•
•
V = 10 V
I = 100 mA = 0.1 A
R = V/I = 10/0.1 = 100 Ω
V = 20 V and I = 200 mA = 0.2 A
R = V/I = 20/0.2 = 100 Ω
Relationship between Current and
Resistance
• For a FIXED voltage,
– The current decreases proportionally to an increase in
resistance
– The current increases proportionally to a decrease in resistance
• The current changes as a result of the change in
resistance
+
+
_
_
• I = V/R
• If V is fixed, current is inversely
proportional to R so
– As R increases, I decreases
• Double the resistance, halve the current.
In-Class Activities
1. What is the effective resistance of each
potentiometer in these circuits?
+
+
A
5V
C
R1
_
B
10 V
A
C
R2
_
B
2. If R1 and R2 actually were the same
potentiometer set to different values and R2
corresponds to C adjusted all the way to the B
end (i.e. total resistance value), what
percentage of the total resistance is R1?
Energy
• Think of a battery like sand in an hour glass
– Sand = charge
• Voltage is the force that moves charge
– Think of gravity on the moon vs the Earth
• Energy = V.Q
– You use much more energy to move sand on Earth than on the
moon where gravity is 1/6th the Earth’s
Power & Energy
• The Instantaneous Power, P, is the
Change of Energy, E, per unit time.
– In our sand analogy, power
is a measure of how quickly
the hourglass is emptying
• Units:
[E] = Joules (J).
[t] = seconds (s).
J
 P    Watt W 
s
E
P
t
Power & Energy
E
P
t
The change in energy can be written as:
E  P  t
We often assume initial energy is zero
Power in terms of Voltage and
Current
Energy
Previously you learned that Voltage 
Charge
E
or V 
Q
Using this and E
yields V  Q  P  t
Q
Since I 
t
 P  t

Q
or V
P
t
then
P V I
Power
- The amount of energy used per unit time
- The battery shown below uses 1 J/s to
generate current – it has used 1 W of
power.
Determining Power
P VI 
Other Power Equations
P V I
V  IR
P I R
In this example,
2
P=
Other Power Equations (continued)
P V I
V
I 
R
V
P 
R
2
In this example,
P=
In-Class Activity for Power and
Ohms Law
• In pairs, complete the following chart
ITEM #
CURRENT
1
10 mA
2
VOLTAGE
RESISTANCE
4W
32 V
16 mW
3.3 kΩ
3
4
15 mA
5
24 mA
POWER
45 V
1.2 kΩ
231 mW
In-Class Activity
Practice Problem 3.11 (p 88)
• Calculate the total energy used by a
1500W dishwasher, a 3600W clothes
dryer, and a 750W air conditioner that are
all being used for 2 hours.
• Report your answer in J and Btu.
• Report your answer in kWh.
• Use the internet to find a recent cost per
kWh and report the total cost for this
problem.
In-Class Activity continued
• If I turn the AC off after 1 hour, how many
kWh do I use?
• If, instead, I told you that the dishwasher
goes through 4 20-minute cycles in the 2
hours (prewash, wash, rinse, dry), each of
which draws 1500W and virtually no power
is used between cycles; how many kWh
do I use?