Electric potential difference

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Electric Circuits

• Electric potential difference
• Electromotive force- emf
• Circuits
• Conductors and resistors
• Resistivity and Resistance
• Circuit Diagrams
• Electric Current DC Circuits
• Measurement

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1. Electric Potential Difference
1). Electric Potential Energy
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1). Potential Energy
In electric field
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1). electric Potential Energy
When E is uniform
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The potential energy per unit charge is called
the electric potential. And
Electric Potential Difference is
SI Unit of Electric Potential joule/coulomb
volt (V)
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19.2 The Electric Potential Difference
DEFINITION OF ELECTRIC POTENTIAL The electric
potential at a given point is the electric
potential energy of a small test charge divided
by the charge itself
SI Unit of Electric Potential joule/coulomb
volt (V)
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2). The Electric Potential Difference
The Accelerations of Positive and Negative
Charges A positive test charge is released from
A and accelerates towards B. Upon reaching B,
the test charge continues to accelerate toward C.
Assuming that only motion along the line is
possible, what will a negative test charge do
when released from rest at B?
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A positive charge accelerates from a region of
higher electric potential toward a region of
lower electric potential. A negative charge
accelerates from a region of lower potential
toward a region of higher potential.
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The Electric Field and Potential Are Related
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2. Electromotive Force emf
emf is the voltage developed by any source of
electrical energy such as a battery or dynamo. It
is generally defined as the potential for a
source in a circuit.  measured in volts
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2. Electromotive Force from Electric battery-
Voltage
Various cells and batteries (top-left to
bottom-right) two AA, one D, one handheld ham
radiobattery, two 9-volt (PP3), two AAA, one C,
onecamcorder battery, one cordless phone battery.
The symbol for a battery in a circuit diagram. It
originated as a schematic drawing of the earliest
type of battery, a voltaic pile.
Line art drawing of a dry cell1. brass cap, 2.
plastic seal, 3. expansion space, 4. porous
cardboard, 5. zinc can, 6. carbon rod, 7.
chemical mixture.
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The SI unit on electric potential difference is
the volt,  V (in honor of Alessandro Volta). 
Within the electrochemical cells of the battery,
there is an electric field established between
the two terminals, directed from the positive
terminal towards the negative terminal. 
The negative terminal is described as the low
potential terminal.
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How battery works In a battery-powered electric
circuit, the chemical energy is used to do work.
Chemical energy is transformed into electric
potential energy within the internal
circuit (i.e., the battery). Once at the high
potential terminal, a positive test charge will
then move through the external circuit and do
work upon the light bulb or the motor or the
heater coils. The positive test charge returns
to the negative terminal at a low energy and low
potential, ready to repeat the cycle (or should
we say circuit) all over again.
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3. Circuits

• An electric circuit is an external path that
  charges can follow between two terminals using a
  conducting material.

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• 1). Requirements 
• the path must be complete and unbroken--There
  must be a closed conducting loop in the external
  circuit that stretches from the high potential,
  positive terminal to the low potential, negative
  terminal.
• The Requirement of an Energy Supply--There must
  be an energy supply capable doing work on charge
  to move it from a low energy location to a high
  energy location and thus establish an electric
  potential difference across the two ends of the
  external circuit.

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Electromotive Force and Current
In an electric circuit, an energy source and an
energy consuming device are connected by
conducting wires through which electric charges
move.
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2). Symbols for circuit elements
A Ideal conductor - generally assume that that
R0 Ideal EMF NOTE device is asymmetric Ideal
Resistor EMF with internal resistance Ideal
Voltmeter - generally assume that that R8 - No
current flows through an ideal voltmeter Ideal
Ammeter - generally assume that that R0
Electrically, an ideal ammeter is a perfect
conductor
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Electronics Demonstrations
http//www.falstad.com/circuit/e-index.html
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Electromotive Force and Current
Within a battery, a chemical reaction occurs that
transfers electrons from one terminal to another
terminal. The maximum potential difference
across the terminals is called the electromotive
force (emf). emf give circuit voltage supply
which is represented by V
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Batteries and Current
The battery pushes current through the circuit. A
battery acts like a pump, pushing charge through
the circuit. It is the circuit's energy
source. Charges do not experience an electrical
force unless there is a difference in electrical
potential (voltage).Therefore, batteries have a
potential difference between their terminals.
The positive terminal is at a higher voltage
than the negative terminal.
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3). Electric Current
The electric current is the amount of charge per
unit time that passes through a surface that is
perpendicular to the motion of the charges.
One coulomb per second equals one ampere (A).
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Current is a concept with wide spread
applications describing the rate of flow of some
quantity that can be
-Throughput of cars per time interval
-water volume coming out of a hose per time
interval
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20.1 Electromotive Force and Current
If the charges move around the circuit in the
same direction at all times, the current is said
to be direct current (dc). If the charges move
first one way and then the opposite way, the
current is said to be alternating current (ac).
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20.1 Electromotive Force and Current
Example 1 A Pocket Calculator The current in a
3.0 V battery of a pocket calculator is 0.17 mA.
In one hour of operation, (a) how much charge
flows in the circuit and (b) how much energy does
the battery deliver to the calculator circuit?
(a)
(b)
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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.
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Electron's journey through a circuit
In the wires of electric circuits, an electron is
the actual charge carrier.
zigzag path that results from countless
collisions with the atoms of the conducting wire
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Conductors Resistance
Some conductors "conduct" better or worse than
others. Reminder conducting means a material
allows for the free flow of electrons. The flow
of electrons is just another name for current.
Another way to look at it is that some
conductors resist current to a greater or lesser
extent. We call this resistance, R. Resistance
is measured in ohms which is noted by the Greek
symbol omega (O)
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Demo
http//phet.colorado.edu/en/simulations/category/p
hysics/electricity-magnets-and-circuits
Battery - resistor circuit
Circuit Construction Kit (DC Only)
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Eg1. 12 C of charge passes a location in a
circuit in 10 seconds. What is the current
flowing past the point?
Eg2. A circuit has 10 A of current.H ow long does
it take 20C of charge to travel through the
circuit?
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Eg3. 20 C of charge passes a location in a
circuit in 30 seconds. What is the current
flowing past the point?
eg4. A circuit has 10 A of current. How much
charge travels through the circuit after 20s?
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Eg5. A circuit has 3 A of current. How long does
it take 45 C of charge to travel through the
circuit?
eg6 A circuit has 2.5 A of current. How much
charge travels through the circuit after 4s?
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• Basic Circuits
• The circuit cannot have gaps.
• The bulb had to be between the wire and the
  terminal.
• A voltage difference is needed to make the bulb
  light.
• The bulb still lights regardless of which side of
  the
• battery you place it on.

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4. Ohms Law
The resistance (R) is defined as the ratio of
the voltage V applied across a piece of material
to the current I through the material.
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4. Ohms Law
OHMS LAW 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
SI Unit of Resistance volt/ampere (V/A) ohm
(O)
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4 Ohms Law
To the extent that a wire or an electrical
device offers resistance to electrical flow, it
is called a resistor.
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4 Ohms Law
Example 1 A Flashlight The filament in a light
bulb is a resistor in the form of a thin piece of
wire. The wire becomes hot enough to emit light
because of the current in it. The
flashlight uses two 1.5-V batteries to provide a
current of 0.40 A in the filament. Determine the
resistance of the glowing filament.
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2. A flashlight has a resistance of 30 O and is
connected by a wire to a 90 V source of voltage.
What is the current in the flashlight?
3. What is the current in a wire whose resistance
is 3 O if 1.5 V is applied to it?
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5. How much voltage is needed in order to
produce a 0.70 A current through a 490 O resistor?
6. How much voltage is needed in order to
produce a 0.5 A current through a 150 O resistor?
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7. What is the resistance of a rheostat coil, if
0.05 A of current flows through it when 6 V is
applied across it?
8. What is the resistance of a rheostat coil, if
20 A of current flows through it when 1000 V is
applied across it?
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5 Resistance and Resistivity
For a wide range of materials, the resistance of
a piece of material of length L and
cross-sectional area A is
resistivity in units of ohmmeter
the measure of a conductor's resistance to
conduct is called its resistivity. Each material
has a different resistivity. Resistivity is
abbreviated using the Greek letter rho
(?). Combining what we know about A, L, and ?, we
can find a conductor's total resistance.
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Resistance, R, is measured in Ohms (O). O is the
Greek letter Omega. Cross-sectional area, A, is
measured in m2 Length, L, is measured in
m Resistivity, ?, is measured in Om
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5 Resistance and Resistivity
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What is the resistance of a good conductor? Low
low resistance means that electric charges are
free to move in a conductor.
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Check Rank the following materials in order of
best conductor to worst conductor. A Iron,
Copper, Platinum B Platinum, Iron, Copper C
Copper, Iron, Platinum
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5 Resistance and Resistivity
Example 3 Longer Extension Cords The
instructions for an electric lawn mower suggest
that a 20-gauge extension cord can be used for
distances up to 35 m, but a thicker 16-gauge cord
should be used for longer distances. The cross
sectional area of a 20-gauge wire is 5.2x10-7Om,
while that of a 16-gauge wire is 13x10-7Om.
Determine the resistance of (a) 35 m of 20-gauge
copper wire and (b) 75 m of 16-gauge copper wire.
(a)
(b)
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3. What is the resistance of a 2 m long copper
wire whose cross-sectional area of 0.2 mm2?
4. An aluminum wire with a length of 900 m and
cross sectional area of 10 mm2 has a resistance
of 2.5 O. What is the resistivity of the wire?
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6. What is the cross-sectional area of a 10O
copper wire of length is 10000 meters ?
7. What is the length of a 10 O copper wire
whose diameter is 3.2 mm?
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20.3 Resistance and Resistivity
Impedance Plethysmography.
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20.3 Resistance and Resistivity
temperature coefficient of resistivity
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20.4 Electric Power
Consider the charge ?q flowing through a battery
where the potential difference between the
battery terminals is V.
energy
power
time
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6. Electric Power
ELECTRIC POWER When there is current in a
circuit as a result of a voltage, the
electric power delivered to the circuit is
SI Unit of Power watt (W)
Many electrical devices are essentially resistors
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Electrical Power Let's think about this
another way... The water at the top has GPE
KE. As the water falls, it loses GPE and the
wheel gets turned, doing work. When the water
falls to the bottom it is now slower, having
done work.
Electric circuits are similar. A charge falls
from high voltage to low voltage. In the process
of falling energy may be used (light bulb, run a
motor, etc).
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Electric Power
Example 5 The Power and Energy Used in
a Flashlight In the flashlight, the current is
0.40A and the voltage is 3.0 V. Find (a) the
power delivered to the bulb and (b) the energy
dissipated in the bulb in 5.5 minutes of
operation.
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20.4 Electric Power
(a)
(b)
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2. A toy car's electric motor has a resistance of
17 O find the power delivered to it by a 6-V
battery.
3. A toy car's electric motor has a resistance
of 6 O find the power delivered to it by a 7-V
battery.
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4. What is the power consumption of a flash light
bulb that draws a current of 0.28 A when
connected to a 6 V battery?
5. What is the power consumption of a flash
light bulb that draws a current of 0.33 A when
connected to a 100 V battery?
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6. A 30O toaster consumes 560 W of power
how much current is flowing through the toaster?
7. A 50O toaster consumes 200 W of power
how much current is flowing through the toaster?
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8. When 30 V is applied across a resistor it
generates 600 W of heat what is the magnitude of
its resistance?
9. When 100 V is applied across a resistor it
generates 200 W of heat what is the magnitude of
its resistance?
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Circuit Diagrams
Note Circuit diagrams do not show where each
part is physically located.
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7. Series Wiring
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.
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Series Wiring
Series resistors
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Series Wiring
Example 8 Resistors in a Series Circuit A 6.00
O resistor and a 3.00 O resistor are connected in
series with a 12.0 V battery. Assuming 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.
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Series Wiring
(a)
(b)
(c)
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Series Wiring
Personal electronic assistants.
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8. Parallel Wiring
Parallel wiring means that the devices
are connected in such a way that the same
voltage is applied across each device.
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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Parallel Wiring
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Parallel Wiring
The two parallel pipe sections are equivalent to
a single pipe of the same length and same total
cross sectional area.
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Parallel Wiring
parallel resistors
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Parallel Wiring
Example 10 Main and Remote Stereo Speakers Most
receivers allow the user to connect to remote
speakers in addition to the main speakers. At
the instant represented in the picture, the
voltage across the speakers is 6.00 V. Determine
(a) the equivalent resistance of the two
speakers, (b) the total current supplied by the
receiver, (c) the current in each speaker, and
(d) the power dissipated in each speaker.
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Parallel Wiring
(a)
(b)
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Parallel Wiring
(c)
(d)
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Parallel Wiring
Conceptual Example 11 A Three-Way Light Bulb and
Parallel Wiring Within the bulb there are two
separate filaments. When one burns out, the bulb
can produce only one level of illumination, but
not the highest. Are the filaments connected in
series or parallel? How can two filaments be
used to produce three different illumination
levels?
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9. Circuits Wired Partially in Series and
Partially in Parallel
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20.9 Internal Resistance
Batteries and generators add some resistance to a
circuit. This resistance is called internal
resistance. The actual voltage between the
terminals of a batter is known as the terminal
voltage.
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20.9 Internal Resistance
Example 12 The Terminal Voltage of a
Battery The car battery has an emf of 12.0 V and
an internal resistance of 0.0100 O. What is the
terminal voltage when the current drawn from the
battery is (a) 10.0 A and (b) 100.0 A?
(a)
(b)
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20.10 Kirchhoffs Rules
The junction rule states that the total current
directed into a junction must equal the total
current directed out of the junction.
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20.10 Kirchhoffs Rules
The loop rule expresses conservation of energy in
terms of the electric potential and states that
for a closed circuit loop, the total of all
potential rises is the same as the total of all
potential drops.
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20.10 Kirchhoffs Rules
KIRCHHOFFS 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 a junction. Loop rule.
Around any closed circuit loop, the sum of the
potential drops equals the sum of the potential
rises.
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20.10 Kirchhoffs Rules
Example 14 Using Kirchhoffs Loop
Rule Determine the current in the circuit.
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20.10 Kirchhoffs Rules
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20.10 Kirchhoffs Rules
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20.10 Kirchhoffs Rules

• Reasoning Strategy
• Applying Kirchhoffs Rules
• Draw the current in each branch of the circuit.
  Choose any direction.
• If your choice is incorrect, the value obtained
  for the current will turn out
• to be a negative number.
• Mark each resistor with a at one end and a at
  the other end in a way
• that is consistent with your choice for current
  direction in step 1. Outside a
• battery, conventional current is always directed
  from a higher potential (the
• end marked ) to a lower potential (the end
  marked -).
• Apply the junction rule and the loop rule to the
  circuit, obtaining in the process
• as many independent equations as there are
  unknown variables.
• 4. Solve these equations simultaneously for the
  unknown variables.

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20.11 The Measurement of Current and Voltage
A dc galvanometer. The coil of wire and pointer
rotate when there is a current in the wire.
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20.11 The Measurement of Current and Voltage
An ammeter must be inserted into a circuit so
that the current passes directly through it.
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20.11 The Measurement of Current and Voltage
If a galvanometer with a full-scale limit of
0.100 mA is to be used to measure the current of
60.0 mA, a shunt resistance must be used so
that the excess current of 59.9 mA can detour
around the galvanometer coil.
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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.
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20.12 Capacitors in Series and Parallel
Parallel capacitors
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20.12 Capacitors in Series and Parallel
Series capacitors
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20.13 RC Circuits
Capacitor charging
time constant
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20.13 RC Circuits
Capacitor discharging
time constant
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20.13 RC Circuits
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20.14 Safety and the Physiological Effects of
Current
To reduce the danger inherent in using circuits,
proper electrical grounding is necessary.