Transcript Chapter 27. Circuits

Chapter 27. Circuits
27.1. What is Physics?
27.2. "Pumping" Charges
27.3. Work, Energy, and Emf
27.4. Calculating the Current in a Single-Loop
Circuit
27.5. Other Single-Loop Circuits
27.6. Potential Difference Between Two
Points
27.7. Multiloop Circuits
27.8. The Ammeter and the Voltmeter
What is Physics?
How can you maintain charges to flow?
“Pumping” Charges
To produce a steady flow of charge, you need a “charge pump” (battery), a
device that—by doing work on the charge carriers—maintains a potential
difference between a pair of terminals. We call such a device an emf
device, and the device is said to provide an emf
does work on charge carriers.
ε , which means that it
The maximum potential difference between the terminals of the
battery is called the electromotive force (emf) ε of the battery
Work, Energy, and Emf
• Within the emf device, positive charge
carriers move from a region of low
electric potential and thus low electric
potential energy. This motion is just
the opposite of what the electric field
between the terminals would cause the
charge carriers to do.
• there must be some source of energy
within the device, enabling it to do
work on the charges by forcing them
to move as they do. The energy source
may be chemical, as in a battery or a
fuel cell. It may involve mechanical
forces, as in an electric generator
•
Emf is:
emf device
• An ideal emf device is one that lacks any internal resistance to
the internal movement of charge from terminal to terminal. The
potential difference between the terminals of an ideal emf
device is equal to the emf of the device.
• A real emf device, such as any real battery, has internal
resistance to the internal movement of charge. When a real emf
device is not connected to a circuit, and thus does not have
current through it, the potential difference between its
terminals is equal to its emf. However, when that device has
current through it, the potential difference between its
terminals differs from its emf.
•If the current flows from the
negative terminal to the
positive terminal of the emf
device, the other types of
energy will be converted to
electrical energy in the circuit;
•If the current flows from the
positive terminal to the
negative terminal of the emf
device, electrical energy in the
circuit will be stored in the emf
device as other types of
energy.
Calculating the Current in a Single-Loop Circuit
• LOOP RULE: The algebraic sum of the changes in
potential encountered in a complete traversal of any loop
of a circuit must be zero.
• RESISTANCE RULE: For a move through a resistance in
the direction of the current, the change in potential is
−iR; in the opposite direction it is +iR.
•
EMF RULE: For a move through an ideal emf device in
the direction of the emf arrow, the change in potential is
+ε; in the opposite direction it is -ε.
Checkpoint
The figure shows the current i in a single-loop circuit
with a battery B and a resistance R (and wires of
negligible resistance), (a) Should the emf arrow at B
be drawn pointing leftward or rightward? At points
a, b, and c, rank (b) the magnitude of the current, (c)
the electric potential, and (d) the electric potential
energy of the charge carriers, greatest first.
Internal Resistance
i

rR
Resistances in Series
• The same electric current
through each device.
• The sum of the potential
differences across the
resistances is equal to the
applied potential difference V.
V=V1+V2+V3.
• Resistances connected in series
can be replaced with an
equivalent resistance Req that
has the same current i and the
same total potential difference
V as the actual resistances.
Example: Resistors in a Series Circuit
A 6.00-W resistor and a 3.00-W resistor are
connected in series with a 12.0-V battery, as Figure
20.16 indicates. Assuming that the battery
contributes no resistance to the circuit, find (a) the
current, (b) the power dissipated in each resistor,
and (c) the total power delivered to the resistors by
the battery.
Resistances in Parallel
• The same voltage is
applied across each
device
• i=i1+i2
• The equivalent
resistance is
Question
In one of the circuits in the drawing, none of the
resistors is in series or in parallel. Which is it?
Explain.
Example 7
A 47.0 W and a 33.0 W resistor are
connected in parallel. What is the equivalent
resistance of the resistors? How much
current would a 12.0 V battery supply to the
network and how much current would flow
through each resistor?
Potential Difference Between Two Points
To find the potential between any two points in a
circuit, start at one point and traverse the circuit to
the other point, following any path, and add
algebraically the changes in potential you encounter.
The terminal-to-terminal potential difference V across the
real battery is different from ε.
Sample Problem
The emfs and resistances in the circuit of Fig. 27-8 a have
the following values:
a) What is the current i in
the circuit?
b) b) What is the potential
difference between the
terminals of battery 1
in Fig. 27-8 a?
Grounding a Circuit
Power, Potential, and Emf
The energy transfer from the
emf device to the outside
charge carriers is
PR  iVab  i R
2
Multiloop Circuits
KIRCHHOFF’S RULES:
• Junction rule. The sum of the magnitudes of the
currents directed into a junction equals the sum of
the magnitudes of the currents directed out of the
junction.
• Loop rule. Around any closed-circuit loop, the sum
of the potential drops equals the sum of the
potential rises.
Sample Problem
Figure 27-11 a shows a multiloop circuit containing one ideal
battery and four resistances with the following values:
(a) What is the current
through the battery?
(b) What is the current i2
through R2?
Sample Problem
Figure 27-12 shows a circuit whose elements have the
following values:
What are the magnitude and direction of the current in
each of the three branches?
The Ammeter and the Voltmeter
Conceptual Questions
1.
The power rating of a 1000-W heater specifies the
power consumed when the heater is connected to an
ac voltage of 120 V. Explain why the power consumed
by two of these heaters connected in series with a
voltage of 120 V is not 2000 W.
2. A number of light bulbs are to be connected to a
single electrical outlet. Will the bulbs provide more
brightness if they are connected in series or in
parallel? Why?