• Potentiometers
• Ohm’s Law Continued
• Power & Energy
EGR 101 1

• How is voltage related to charge and energy?
• What is the formula for resistance?
• What is Ohm’s Law?
• What does it mean?
EGR 101 2

• 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
EGR 101 3

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
A
B/C
• As a voltage divider
(to be covered in a later lecture)
EGR 101 4

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):
EGR 101 5

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?
EGR 101 6

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
+ +
_ _
EGR 101 7

1. What is the effective resistance of each potentiometer in these circuits?
+
5 V
_
C
A
R
1
B
+
10 V
_
C
A
R
2
B
2. If R
1 and R
2 actually were the same potentiometer set to different values and R
2 corresponds to C adjusted all the way to the B end (i.e. total resistance value), what percentage of the total resistance is R
1
?
EGR 101 8

• 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 1/6 th the Earth’s
EGR 101 9

• The Instantaneous Power, P , is the
Change of Energy, E , per unit time.
– In our sand analogy, power 
E is a measure of how quickly P
 the hourglass is emptying
 t
• Units: [ E ] = Joules ( J ).
[ t ] = seconds ( s ) .
  
J s
  
EGR 101 10

P


E
 t
The change in energy can be written as:

E

P
  t
We often assume initial energy is zero
EGR 101 11

Power in terms of Voltage and
Current
Previously you learned that Voltage

Energy
Charge or V


E

Q
Using this and

E

P
  t yields V
 
Q

P
  t or V


Q t

P
Since I


Q
 t then P

V I
EGR 101 12

- 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.
EGR 101 13

P

VI

EGR 101 14

P

V I
V

IR

2 P I R
In this example,
P =
EGR 101 15

Other Power Equations (continued)
P

V I
I
P

V
R

V
R
2
In this example,
P =
EGR 101 16