Understanding Electric Circuits: Current, Voltage, and Resistance

L 25 Electricity and Magnetism [3]
 
Electric circuits
what conducts electricity
what does and doesn’t conduct electricity
Current, voltage and resistance
Ohm’s Law
Power loss due to heat produced in a
resistor
Simple circuit connections
 
1
Electric current (symbol 
I)
 
q
2
Examples
 
A charge of 1 microcoulomb (10
6
 C)
passes through a wire every millisecond
(10
3
 s). What is the current in the wire?
I = q/t = 
10
6
 C/10
3
 s = 10
6+3
 s = 10
3
 A
 
            =  1 milliamp = 1 mA
 
A current of 3 A flows in a wire. Over a
period of 1 minute, how much charge
passes a given point in the wire?
 q = I 
t = 3 A 
 60 s = 180 C
3
Potential difference or
Voltage (symbol V)
 
To make water flow in a pipe, a pressure
difference must be applied between the
ends of the pipe
A potential difference or 
voltage
 
must be
applied between the ends of a conductor
to make the electrons flow
Voltage is supplied by a battery (DC) or a
an electrical outlet (AC)
4
Electrical resistance (symbol R)
 
Conductors have “free electrons” that roam
around randomly 
 no current
To push these free electrons through a
conductor, i,e., to make a 
current
, some
external force must be applied to the conductor
This external force must be continually applied
because the electrons experience a 
resistance
 to
motion, because they keep bumping into the
atoms and slowing down
The slowing down of the electrons is called
“resistance”  
(R) 
and is measured in Ohms 
(
)
The battery provides the external force
(voltage) 
that keeps the electrons moving
5
Electrons pass through an obstacle
course in a conductor
 
atoms
 
electron
 
path
 
T
h
e
 
r
e
s
i
s
t
a
n
c
e
 
(
R
)
 
i
s
 
a
 
m
e
a
s
u
r
e
 
o
f
 
t
h
e
 
d
e
g
r
e
e
 
t
o
   which the conductor impedes the flow of current
 We use the symbol                            to represent
   the electrical  resistance in a circuit
6
 
A battery is a charge pump
 
7
Direction of current flow
 
By convention, the current direction is taken
as the direction that positive charges would
flow, so it is 
opposite
 to the electron flow
 
R
8
Current, Voltage and Resistance: OHM’S LAW
 
Ohm’s law
 is a relation between current (
I
), voltage (V)
and resistance (R)
I
 = Voltage / Resistance   =  V / R
V in volts (V), R in ohms (
), 
I 
in amps (A)
 
equivalent forms:
   
V = 
I
 R,     
I 
= V / R,     R = V / 
I
R could represent, the
resistance of a light bulb,
hair dryer, coffee pot,
vacuum cleaner, etc.
9
Examples
(1)
If a 3 volt flashlight bulb has a resistance of 9 ohms,
how much current will it draw?
   I = V / R =  3 V / 9 
  = 1/3  A (Ampere)
(2)  If a light bulb draws 2 A of current when connected to a
120 volt circuit, what is the resistance of the light bulb?
  
R = V / I = 120 V / 2 A = 60 
  (Ohms)
10
Heat produced in a resistor
 
As we have seen before, friction causes heat
The collisions between the electrons and the atoms in a
conductor produce heat 
 wires get 
warm
 when they
carry currents: 
in an electric stove
this heat is used for cooking
The amount of energy converted to heat each second is
called the 
power loss in a resistor
If the resistor has a voltage 
V
 across it and carries a
current 
I
, 
the electrical power converted to heat is given by
Power:  P = I 
 V 
= I 
(I 
 R) 
= 
 I
2
 
 R
 
From Ohm’s law
11
Heat produced in a resistor
 
Power 
 
 
P = 
I
 
V or 
I
2
 
 R
Power is measured in 
Watts = amps 
 
volts
One Watt is one Joule per second
Wires are rated for the maximum current that
can be handled based on how hot it can get
To carry more current you need wire of a larger
diameter 
 this is called the wire gauge, the
lower the gauge the more current it can carry
Using extension cords can be dangerous!
12
examples
How much current is drawn by a 60 Watt light
bulb connected to a 120 V power line?
Solution: 
P = 60 W = I 
V = I 
 120
    
so I =
 
0.5 Amps (A)
What is the resistance of the bulb?
Solution:
 V = I R
  120 V = ½ A 
 R
   
     so R = 240 
,  or R = V/I
How much current is used by a 2000 W hair dryer
plugged into a 120 V power source?
 
P = I V 
 I = P / V = 2000W / 120 V 
 17 A
13
extension cords and power strips
 
extension cords are rated for maximum
current 
 you must check that whatever is
plugged into it will not draw more current
than the cord can handle safely.
power strips are also rated for 
maximum
current
 
 since they have multiple inputs
you must check that the total current
drawn by everything on it does not exceed
the posted 
current rating
14
Unsafe practices
 
Must have capacity to carry all current
15
Parallel and Series Connections
 
P
a
r
a
l
l
e
l
 
c
o
n
n
e
c
t
i
o
n
All bulbs have the
same voltage = 12 V.
The current provided
by the battery is
divided equally
among the 3 light
bulbs.
 
S
e
r
i
e
s
 
c
o
n
n
e
c
t
i
o
n
The same current
passes through each
light bulb.
Each bulb has a voltage
of 4 V across it.
16
Simple direct current (DC)
electric circuits
E
x
e
r
c
i
s
e
:
 
g
i
v
e
n
 
a
 
b
a
t
t
e
r
y
,
 
s
o
m
e
 
w
i
r
e
 
a
n
d
 
a
light bulb, connect them so that the bulb is on
.
 
The battery polarity
+/- does not matter,
Either way the bulb
Will be on.
17
Electric circuits - key points
 
Electrons carry the current in a conductor
a circuit provides a closed path for the electrons to
circulate around
Conductors have a property called resistance which
impedes the flow of current
the battery is like a pump that re-energizes the electrons
each time they pass through it
Ohm’s law is the relation between current, voltage and
resistance:  
V = I R
When current passes through a wire, the wire
heats up, the amount of heat energy produced
each second (Power) is  
P = I V = I
2 
R
18
What is DC (direct current) ?
 
With DC or direct current the current
always flows in the same direction
this is the type of current you get when
you use a battery as the voltage source.
the direction of the current depends on
how you connect the battery
the electricity that you get from the power
company is not DC it is AC (alternating).
We will discuss AC in the next lecture
19
connecting batteries
 do’s and don’ts
 
don’t connect a wire from the + side to the – side,
this shorts out the battery and will make it get hot
and will shorten its lifetime.
Do not
do this
20
dueling batteries
 
The batteries are trying to push currents in
opposite directions 
 they are working against
each other. This does not work.
Do not
do this
21
Proper battery connections
Connecting two 1.5 volt batteries 
gives like this gives 3.0 volts. 
22
 
A Flashlight!
Batteries in parallel
 
This connection still
gives 1.5 volts but
since there are 2
batteries 
it will provide
electrical current
for a 
longer
 time
23
Longer lasting power
series and parallel combination
 
This connection provides 3.0 volts and will
provide power for a longer amount of time
S
e
r
i
e
s
 
c
o
n
n
e
c
t
i
o
n
 
[
 
 
+
 
 
+
 
]
 
g
i
v
e
s
 
3
.
0
 
V
P
a
r
a
l
l
e
l
 
c
o
n
n
e
c
t
i
o
n
 
[
 
 
+
 
 
]
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
[
 
 
 
+
 
 
]
provides 3.0 V
24
Disposable 
vs.
 Rechargeable Batteries
 
Disposable batteries 
are electrochemical
cells that convert chemical energy into
electrical energy. Because the electrode
materials are irreversible changed during
discharge, they must be replaced
Rechargeable batteries 
are also electro-
chemical cells, but use materials in which
the chemical reactions can be reversed in
the recharging process
 
25
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Electric circuits involve the flow of electric current through conductors with varying levels of resistance. Current (I) is the amount of charge passing through a point in a wire per unit of time, measured in amperes. Voltage (V) is the potential difference required to make electrons flow in a conductor, supplied by a battery or electrical outlet. Resistance (R) is the impedance to current flow caused by electrons colliding with atoms, measured in Ohms. Ohm's Law relates current, voltage, and resistance. Power loss in circuits is due to heat generated in resistors.


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  1. L 25 Electricity and Magnetism [3] Electric circuits what conducts electricity what does and doesn t conduct electricity Current, voltage and resistance Ohm s Law Power loss due to heat produced in a resistor Simple circuit connections 1

  2. Electric current (symbol I) Electric current is the flow of electric charge q q It is the amount of charge q that passes a given point in a wire in a time t: I =? ? Current is measured in amperes 1 ampere (A) = 1 C / 1 s 2

  3. Examples A charge of 1 microcoulomb (10 6 C) passes through a wire every millisecond (10 3 s). What is the current in the wire? I = q/t = 10 6 C/10 3 s = 10 6+3 s = 10 3 A = 1 milliamp = 1 mA A current of 3 A flows in a wire. Over a period of 1 minute, how much charge passes a given point in the wire? q = I t = 3 A 60 s = 180 C 3

  4. Potential difference or Voltage (symbol V) To make water flow in a pipe, a pressure difference must be applied between the ends of the pipe A potential difference or voltage must be applied between the ends of a conductor to make the electrons flow Voltage is supplied by a battery (DC) or a an electrical outlet (AC) 4

  5. Electrical resistance (symbol R) Conductors have free electrons that roam around randomly no current To push these free electrons through a conductor, i,e., to make a current, some external force must be applied to the conductor This external force must be continually applied because the electrons experience a resistance to motion, because they keep bumping into the atoms and slowing down The slowing down of the electrons is called resistance (R) and is measured in Ohms ( ) The battery provides the external force (voltage) that keeps the electrons moving 5

  6. Electrons pass through an obstacle course in a conductor atoms path electron The resistance (R) is a measure of the degree to which the conductor impedes the flow of current We use the symbol to represent the electrical resistance in a circuit 6

  7. A battery is a charge pump 7

  8. Direction of current flow I I R resistor I I Duracell I I + By convention, the current direction is taken as the direction that positive charges would flow, so it is opposite to the electron flow 8

  9. Current, Voltage and Resistance: OHMS LAW Resistance R R could represent, the resistance of a light bulb, hair dryer, coffee pot, vacuum cleaner, etc. Current I + Battery voltage V Ohm s law is a relation between current (I), voltage (V) and resistance (R) I = Voltage / Resistance = V / R V in volts (V), R in ohms ( ), I in amps (A) equivalent forms:V = I R, I = V / R, R = V / I 9

  10. Examples (1) If a 3 volt flashlight bulb has a resistance of 9 ohms, how much current will it draw? I = V / R = 3 V / 9 = 1/3 A (Ampere) (2) If a light bulb draws 2 A of current when connected to a 120 volt circuit, what is the resistance of the light bulb? R = V / I = 120 V / 2 A = 60 (Ohms) 10

  11. Heat produced in a resistor As we have seen before, friction causes heat The collisions between the electrons and the atoms in a conductor produce heat wires get warm when they carry currents: in an electric stove this heat is used for cooking The amount of energy converted to heat each second is called the power loss in a resistor If the resistor has a voltage V across it and carries a current I, the electrical power converted to heat is given by Power: P = I V = I (I R) = I2 R From Ohm s law 11

  12. Heat produced in a resistor Power P = I V or I2 R Power is measured in Watts = amps volts One Watt is one Joule per second Wires are rated for the maximum current that can be handled based on how hot it can get To carry more current you need wire of a larger diameter this is called the wire gauge, the lower the gauge the more current it can carry Using extension cords can be dangerous! 12

  13. examples How much current is drawn by a 60 Watt light bulb connected to a 120 V power line? Solution: P = 60 W = I V = I 120 so I =0.5 Amps (A) What is the resistance of the bulb? Solution: V = I R 120 V = A R so R = 240 , or R = V/I How much current is used by a 2000 W hair dryer plugged into a 120 V power source? P = I V I = P / V = 2000W / 120 V 17 A 13

  14. extension cords and power strips extension cords are rated for maximum current you must check that whatever is plugged into it will not draw more current than the cord can handle safely. power strips are also rated for maximum current since they have multiple inputs you must check that the total current drawn by everything on it does not exceed the posted current rating 14

  15. Unsafe practices Must have capacity to carry all current 15

  16. Parallel and Series Connections Parallel connection All bulbs have the same voltage = 12 V. The current provided by the battery is divided equally among the 3 light bulbs. + 12 V Series connection The same current passes through each light bulb. Each bulb has a voltage of 4 V across it. + 12 V 16

  17. Simple direct current (DC) electric circuits Exercise: given a battery, some wire and a light bulb, connect them so that the bulb is on. The battery polarity +/- does not matter, Either way the bulb Will be on. 1.5 V 17

  18. Electric circuits - key points Electrons carry the current in a conductor a circuit provides a closed path for the electrons to circulate around Conductors have a property called resistance which impedes the flow of current the battery is like a pump that re-energizes the electrons each time they pass through it Ohm s law is the relation between current, voltage and resistance: V = I R When current passes through a wire, the wire heats up, the amount of heat energy produced each second (Power) is P = I V = I2 R 18

  19. What is DC (direct current) ? With DC or direct current the current always flows in the same direction this is the type of current you get when you use a battery as the voltage source. the direction of the current depends on how you connect the battery the electricity that you get from the power company is not DC it is AC (alternating). We will discuss AC in the next lecture 19

  20. connecting batteries do s and don ts don t connect a wire from the + side to the side, this shorts out the battery and will make it get hot and will shorten its lifetime. + Do not do this Duracell 20

  21. dueling batteries Do not do this + Duracell Duracell + The batteries are trying to push currents in opposite directions they are working against each other. This does not work. 21

  22. Proper battery connections Connecting two 1.5 volt batteries gives like this gives 3.0 volts. Duracell Duracell + + A Flashlight! 22

  23. Batteries in parallel This connection still gives 1.5 volts but since there are 2 batteries it will provide electrical current for a longer time Duracell + Duracell + 1.5 V D Cell 23

  24. Longer lasting power series and parallel combination + + 1.5 V 1.5 V Series connection [ + + ] gives 3.0 V + + 1.5 V 1.5 V Parallel connection [ + ] [ + ] provides 3.0 V This connection provides 3.0 volts and will provide power for a longer amount of time 24

  25. Disposable vs. Rechargeable Batteries Disposable batteries are electrochemical cells that convert chemical energy into electrical energy. Because the electrode materials are irreversible changed during discharge, they must be replaced Rechargeable batteries are also electro- chemical cells, but use materials in which the chemical reactions can be reversed in the recharging process 25

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