Download LectureOutline-Circuits [Compatibility Mode]

2/25/2014
Circuits
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20.1 Electromotive Force and Current
Conventional current is the hypothetical flow of positive charges that would
have the same effect in the circuit as the movement of negative charges that
actually does occur.
Current
Conservation of current
Batteries
Resistance and resistivity
Simple circuits
Sample question:
How can the measurement of an electric current passed through a
person’s body allow a determination of the percentage body fat?
Properties of a Current
Conservation of Current
Definition of a Current
Rank the bulbs in the following circuit according to their brightness,
from brightest to dimmest.
The wires below carry currents as noted. Rate the currents IA, IB
and IC:
A. I A > I B > I C
B. I B > I A > I C
C. I C > I A > I B
D. I A > I C > I B
E. I C > I B > I A
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20.3 Resistance and Resistivity
Batteries
The potential difference
between the terminals of a
battery, often called the
terminal voltage, is the
battery’s emf.
Wchem
∆Vbat = ____
=ε
q
R=ρ
Simple Circuits
L
A
Checking Understanding
The current is determined by
the potential difference and
the resistance of the wire:
I =
∆V
_____
chem
R
A battery is connected to a wire, and makes a current in the wire.
i.
Which of the following changes would increase the
current?
ii. Which would decrease the current?
iii. Which would cause no change?
Increasing the length of the wire
Keeping the wire the same length, but making it thicker
Using a battery with a higher rated voltage
Making the wire into a coil, but keeping its dimensions the
same
E. Increasing the temperature of the wire
A.
B.
C.
D.
20.3 Resistance and Resistivity
Resistivity
Impedance Plethysmography.
The resistance of a wire
depends on its dimensions
and the resistivity of its
material:
R=ρ
L
L
L2
=ρ
=ρ
A
Vcalf L
Vcalf
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20.2 Ohm’s Law
Electric Blankets
OHM’S LAW
1. An electric blanket has a wire that runs through the interior. A
current causes energy to be dissipated in the wire, warming the
blanket. A new, low-voltage electric blanket is rated to be used at
18 V. It dissipates a power of 82 W. What is the resistance of the
wire that runs through the blanket?
The ratio V/I is a constant, where V is the
voltage applied across a piece of material
and I is the current through the material:
V
= R = constant
I
V = IR
or
2. For the electric blanket of the above example, as the temperature
of the wire increases, what happens to the resistance of the wire?
How does this affect the current in the wire? The dissipated
power?
SI Unit of Resistance: volt/ampere (V/A) = ohm (Ω)
20.4 Electric Power
Series Resistors
Consider the charge ∆q flowing through a battery where the potential difference
between the battery terminals is V.
energy
P=
(∆q )V
∆t
=
∆q
V = IV
∆t
power
time
20.4 Electric Power
Parallel Resistors
ELECTRIC POWER
When there is current in a circuit as a result of a voltage, the electric
power delivered to the circuit is:
P = IV
SI Unit of Power: watt (W)
Many electrical devices are essentially resistors:
P = I (IR ) = I 2 R
V2
V 
P =  V =
R
R
 
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Kirchhoff’s Laws
Measuring Body Fat
The resistivity of the body is a good measure of its overall composition. A
measure of the resistance of the upper arm is a good way to estimate the percent
fat in a person’s body. Let’s model a person’s upper arm as a cylinder of diameter
8.0 cm and length 20 cm. We can model the composition of the arm by assuming
that the muscle, far, and nonconductive portions (the bone) form simple regions.
This simple model actually works quite well. For a typical adult, the bone has a
cross-sectional area of 1.0 cm2; to a good approximation, the balance of the arm
is fatty tissue or muscle.
A. Assume that the arm has 30% fat and 70% muscle. What is the resistance of
the arm?
B. Now, assume that the arm has only 10% muscle. What is the resistance
now?
The measurement of the resistance of the arm is made by applying a voltage and
measuring a current. Too much current can be uncomfortable and, as we will see,
can be dangerous. Suppose we wish to limit the current to 1.0 mA. For each of
the above cases, what is the maximum voltage that could be employed?
20.6 Series Wiring
20.8 Circuits Wired Partially in Series and Partially in Parallel
There are many circuits in which more than one device is connected to
a voltage source.
Series wiring means that the devices are connected in such a way
that there is the same electric current through each device.
20.7 Parallel Wiring
Parallel wiring means that the devices are
connected in such a way that the same
voltage is applied across each device.
20.11 The Measurement of Current and Voltage
An ammeter must be inserted into
a circuit so that the current passes
directly through it.
When two resistors are connected in
parallel, each receives current from the
battery as if the other was not present.
Therefore the two resistors connected in
parallel draw more current than does either
resistor alone.
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20.11 The Measurement of Current and Voltage
To measure the voltage between two points
in a circuit, a voltmeter is connected between
the points.
20.7 Parallel Wiring
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