Download emf and the terminal voltage

Chapter 19
DC Circuits
Units of Chapter 19
• EMF and Terminal Voltage
• Resistors in Series and in Parallel
• Kirchhoff’s Rules
• EMFs in Series and in Parallel; Charging a
Battery
• Circuits Containing Capacitors in Series
and in Parallel
Units of Chapter 19
• RC Circuits – Resistor and Capacitor in
Series
• Electric Hazards
• Ammeters and Voltmeters
Objectives: The students will be able to:
•Distinguish between the emf and the terminal
voltage of a battery and calculate the terminal
voltage given the emf, internal resistance of the
battery, and external resistance in the circuit.
•Determine the equivalent resistance of
resistors arranged in series or in parallel or the
equivalent resistance of a series parallel
combination.
Resistors in circuits
 To
determine the current or voltage in a
circuit that contains multiple resistors,
the total resistance must first be
calculated.
 Explain
that resistors can be combined
in series or parallel.
19.1 EMF and Terminal Voltage
Electric circuit needs battery or generator to
produce current – these are called sources of
emf.
Battery is a nearly constant voltage source, but
does have a small internal resistance, which
reduces the actual voltage from the ideal emf:
(19-1)
19.1 EMF and Terminal Voltage
This resistance behaves as though it were in
series with the emf.
EMF vs. Terminal Voltage
• For current to flow through a circuit, we need a device to
supply the electrical energy, ie: a battery
• A device that supplies electrical energy to a circuit is
called the source of what is referred to as the
Electromotive Force or EMF ( )
• EMF is a misnomer because the battery does not deliver
a force in Newtons
• The potential difference ΔV=Vab , is measured across the
terminals of a battery
• When no current is drawn
from the battery, Vab = 
which is determined from
the chemical reactions in
the battery
Internal Resistance
• The battery is not a constant source of current because
of internal losses within the battery
• The chemical reaction that produces the electrical
energy also produces heat, and may be modeled as a
resistor internal to the battery. This is called the internal
resistance “r”.
Battery Circuit
Vab  V    I  r
where I 

Rr
• The terminal voltage is always smaller than the EMF
Practice problem – p.521
Circuits
• Can either be series or
parallel.
Series Circuit
• Three lamps connected in a daisy-chain fashion
can be considered as three resistors in series
Series
• Current only takes one
path for electrons
• Current flows through
every part of the circuit
Lights in a Series
Series
• If you add a resistor (like
another light):
–Total resistance goes UP
since all the current has must
go through each resistor.
Adding Resistors to
Series:
–Current in the circuit will
go DOWN (lights will dim)
–If you remove a light bulb
or one burns out—all go
out!
Current in Series
• Current is the same at all
points
• Use Ohm’s Law to find
current using resistance
and voltage
19.2 Resistors in Series and in Parallel
A series connection has a single path from
the battery, through each circuit element in
turn, then back to the battery.
19.2 Resistors in Series and in Parallel
The current through each resistor is the same;
the voltage depends on the resistance. The
sum of the voltage drops across the resistors
equals the battery voltage.
(19-2)
19.2 Resistors in Series and in Parallel
From this we get the equivalent resistance (that
single resistance that gives the same current in
the circuit).
(19-3)
Resistors in Series
 When
connected in series, the total
resistance (Rt) is equal to:
Rt = R1 + R2 + R3 +…
 The
total resistance is always larger
than any individual resistance because
all of the current must go through each
resistor.
Sample Problem
Calculate the total
current through the
circuit.
15 Ω 10 Ω 6 Ω
Rt = 15 Ω +10 Ω + 6 Ω
Rt = 31 Ω
I = V/Rt = 10 V/ 31 Ω = 0.32 A
10 V
Resistors in Series

Since charge has only one path to flow
through, the current that passes through
each resistor is the same.

The sum of all potential differences equals
the potential difference across the battery.
> R value = > V Value
5V
3V
2V
10 V
Resistance in series circuits
Use Ohm’s law to calculate the voltage
across the resistors in the next slide.
Write your values in the voltmeters and see
if they agree with the actual readings.
.603
Amps
2.2 Ω
1.5 Ω
.897
1.332
Volts
Volts
What should the
voltage across the
two resistors be?
.601
Amps
2.2 Ω
1.5 Ω
2.231
Volts
Equivalent resistance
The two resistors in the previous series
circuit can be thought of as a single resistor.
Work out and write the equivalent
resistance using Ohm’s law and the values
of current and voltage shown.
2.231 V
3.7 Ω
0.601 A
Equivalent resistance
In a series circuit the total resistance of the
components is the sum of the resistance of each
component. So, the equivalent resistance R is found
as:
R = R1 + R2
R1
R2
R
2.2 Ω
1.5 Ω
3.7 Ω
19.2 Resistors in Series and in Parallel
A parallel connection splits the current; the
voltage across each resistor is the same:
Parallel Circuits
Has
at least one point
where current divides
More than one path for
current to flow
Paths are also known as
branches
Lights in Parallel
Parallel:
If
you add a resistor:
Total resistance goes
down
Total current goes up
when you add
another path
Removing a Light
Bulb
If
you remove a light
bulb or one burns out,
the others stay on
because the circuit is
still closed.
Current in Parallel
Current
flows into a
branching point, the
same total current must
flow out again
Current depends on
resistance in each
branch
Voltage in Parallel
Voltage
is the
same across each
branch – because
each branch is on
the same wire
Resistance in
Parallel
Calculate
current in
each branch based on
resistance in each
branch by using
Ohm’s Law
Parallel Circuit
• Three lamps connected across each other can be
modeled as three resistors in parallel
R1R2
• For only 2 resistors in parallel, Req becomes: Req 
R1  R2
19.2 Resistors in Series and in Parallel
The total current is the sum of the currents
across each resistor:
19.2 Resistors in Series and in Parallel
This gives the reciprocal of the equivalent
resistance:
(19-4)
Resistors in Parallel
 When
connected in parallel, the total
resistance (Rt) is equal to:
1/Rt = 1/R1 + 1/R2 + 1/R3 +…
 Due
to this reciprocal relationship, the
total resistance is always smaller than
any individual resistance.
Sample Problem
Calculate the total
resistance through this
segment of a circuit.
1/Rt = 1/12 Ω +1/4 Ω + 1/6 Ω
12 Ω
4Ω
= 1/12 Ω + 3/12 Ω + 2/12 Ω
1/Rt = 6/12 Ω = ½ Ω
Rt = 2 Ω
6Ω
Resistors in Parallel
 Since
there is more than one possible
path, the current divides itself
according to the resistance of each
path.
smallest resistor = more current passes
largest resistor = least current passes
Resistors in Parallel
 The
voltage across each resistor in a
parallel combination is the same.
10 V
10 V
10 V
10 V
Calculate the total resistance in the
circuit below
3Ω
2Ω
6Ω
4Ω
Rtot = 3 Ω + 2 Ω = 5 Ω
Rtot = 6 Ω + 4 Ω = 10 Ω
Rtot = 3 1/3 Ω
+
-
1/Rtot = 2/10 Ω+ 1/10 Ω = 3/10 Ω
Resistance in parallel circuits
Look at the parallel circuit on the next slide
and work out the current in the main circuit
and through each resistor in the parallel
branches.
What do you think
the current in the
main circuit should
be?
1.830
1.991
Volts
Amps
2.2 Ω
0.832 A
1.716
Volts
1.144 A
1.5 Ω
Resistance in parallel circuits
The current in the
main circuit is the
sum of the currents
in the parallel
branches:
I
I1
R1
I2
R2
I = I 1 + I2
19.2 Resistors in Series and in Parallel
An analogy using
water may be helpful
in visualizing
parallel circuits:
Gravitational potential difference is
the same for both pipes, just as
voltage is the same for parallel
resistors. If both pipes are open,
twice as much water will flow
through. With two equal pipes open,
the net resistance to the flow of
water will be reduced, by half, just
as for electrical circuits in parallel.
If both pipes are closed, the dam offers infinite resistance to the flow of water.
This corresponds in the electrical case to an open circuit, no current- infinite
resistance.
Toll Road—Circuit
Analogy
Toll Booth
Explanation
 Adding
toll booths in series
increases resistance and
slows the current flow.
 Adding toll booths in
parallel lowers resistance
and increases the current
flow.
Batteries in Series
and Parallel:
In
series—The voltage
is increased.
In parallel—No
change in voltage;
these batteries will
last longer!
Homework




Questions chapter 19
#1, 4, 7
Problems
#1, 5, 7, 9, 15, 17
Elaboration

Physics Classroom activities

phET activities