Transcript Batteries are made of conducting material and thus have resistance

DC CIRCUITS
Batteries and Lights
Batteries and Terminal Voltage
Batteries consist of plates that are
charged by a chemical reaction taking
place between the plates.
The reaction provides the energy to lift
charges from a low potential to a high
potential.
The emf created by the chemical
reaction is a potential difference that
drives electrical devices attached to the
battery.
Like other sources of power, batteries
are not 100% efficient.
++ ++
Reaction
−− −−
Batteries and Terminal Voltage
Batteries are made of conducting
material and thus have resistance.
The resistance inside a battery is called
the internal resistance r .
The emf of the battery is a theoretical
potential that would be reached if there
were no resistance.
The actual potential produced by a
battery is less than the emf due to the
loss created by the internal resistance.
The actual potential is called the terminal voltage.
++ ++
Reaction
−− −−
Batteries and Terminal Voltage
The terminal voltage is the potential
difference between the terminals (ends)
of a battery.
V
ε
I
r
V = e - Ir
++ ++
Terminal voltage
emf
Current in battery
Internal Resistance
−− −−
If the internal resistance is negligible
(often the case in most problems)
Reaction
V =e
Graph of Terminal Voltage V = e - Ir
The equation for terminal voltage is linear.
To determine the exact look of the graph simply rearrange the
equation to match y = mx + b .
If asked for the voltage vs. current graph of a battery
y = mx + b
V = -rI + e
ε
V
−r
The y-intercept is emf
The slope is negative
The slopes value is the internal resistance.
I
Example 3
A battery has an emf of 6.0 V and an internal resistance
of 0.10 Ω. Determine the terminal voltage if a 3.0 A
current runs through the battery.
V = e - Ir
( ) ( )(
V = 6.0 - 3.0 0.10
V = 5.7 V
)
When Internal Resistance is Negligible
Unless told otherwise: Internal resistance is negligible, r = 0
V = e - Ir
V =e
When working with batteries Ohm’s Law and the power
equations modify as follows
V = IR
P = IV
e = IR
P = Ie
Household Wiring
Homes are wired in parallel.
When you turn lights or appliances on and off the other
lights in your house do not get brighter or dimmer.
If one light goes out the others remain lit.
This is because they are on different parallel circuits.
Household Wiring
However, there is a down side.
As each new device is turned on you use more and more power
increasing the amount of current flowing in the wires.
Flowing currents involve collisions and these generate heat.
The wires can become hot enough to start a fire.
Therefore, one device in the circuit is wired in series.
Circuit Breakers (in some circuits fuses are used)
Circuit breakers and fuses are a devices that turns the current
off if the circuit is overloaded.
Light Bulbs in Circuits
Light bulbs are sold by their wattage which is related to the power
consumption of the bulb, and we buy lights with a higher wattage to
get brighter lights.
Light bulbs sold in the USA are intended for a 120 V parallel circuit,
and in these circuits higher wattage means brighter bulbs.
However, if you wire the same bulbs in series, or use then in European
240 V circuits, you will not draw the wattage stamped on the bulb.
Wattage is not fixed!
Light bulbs are actually resistors, and it is their resistance that follows
the bulb from circuit to circuit.
Find the resistance and transfer this to each new circuit.
Light Bulbs in Circuits
A 120 W light and 240 W light are
connected into a USA 120 V parallel
circuit.
V
I
R
P
ε
120
3
40
360
Power adds.
L1
120
1
120
120
Parallel: voltage stays the same.
L2
120
2
60
240
V
I
R
P
Use P = IV to find current.
Use V = IR to find resistance
ε
120
The resistance of RL1 and RL2 are the
constant property.
L1
120
This property moves to other circuits
L2
60
Light Bulbs in Circuits
Connect the same light into a
120 V series circuit.
Find total resistance
RS = SRi
V
I
R
P
ε
120
3
40
360
L1
120
1
120
120
L2
120
2
60
240
V
I
R
P
Use V = IR to find the total
current.
In series current stays the same.
Use V = IR to find voltage.
ε
120 0.67 180
L1
80
0.67 120 53.3
L2
40
0.67
60
26.7
V
I
R
P
80
Use P = IV to find power.
Power in series does not match
the power printed on the bulb.
ε
Resistance is the only constant.
L1
120
L2
60
240
40
Light Bulbs in Circuits
Now the bulbs are connected in
a 240 V parallel circuit.
Find total resistance.
1
1
=S
RP
Ri
V
I
R
P
ε
120
3
40
360
L1
120
1
120
120
L2
120
2
60
240
V
I
R
P
Use V = IR to find total current
Parallel: voltage stays the same.
ε
120 0.67 180
Use V = IR to find current.
L1
80
0.67 120 53.3
L2
40
0.67
60
26.7
V
I
R
P
ε
240
6
40
1440
L1
240
2
120
480
L2
240
4
60
960
Use P = IV to find power.
Let’s compare power and
resistance for all three scenarios.
80
Light Bulbs in Circuits
V
ε
What is the same for the light
bulbs no matter what circuit
they are in?
In a series circuit the light
labeled 240 W actually drew half
the power of the 120 W light.
To avoid wrong answers find the
resistance of a light and then
find the true power used.
R
P
120 V parallel
L1
120
120
L2
60
240
R
P
Resistance
The printed wattage on light
bulbs is only true if used in a
120 V parallel circuit.
I
V
ε
I
120 V series
L1
120 53.3
L2
60
26.7
R
P
V
ε
I
240 V parallel
L1
120
480
L2
60
960