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17 Electric Potential
This section covers the use of electricity for energy, and applies the law of conservation of energy
17.1 Electric Potential Energy and Potential Diﬀerence Electric Potential Energy
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The work done by an electric field to move a charge a distance is
W = Fd = qEd
Where F is force of the electric field, d is the distance moved, q is the charge, and E is the electric field
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Change in electic potential energy is the negative of the work done by electric force
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Note the previous two equations apply only to a uniform electric field
Electric Potential and Potential Diﬀerence
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ELectric Potential -ELectric potential energyper unit charge, calculated by
Which represents the potential energy of a charge at a point a divided by the magnitude of the charge
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Diﬀerence in Potential -Only diﬀerences in potential energy are maeningful, this is the diﬀerence in potential energy of two points a and b
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When a force does mechanical work, the change in potential between points a and b is
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Voltage -Another name for potential diﬀerence, measured in volts
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Change in potential energy is equal to the product of the charge and volatge
Δ = qVba
17.2 Relation Between Electric Potential and Electric Field
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Work done by an electric field is the negative of the charge times voltage,
W
= −qVba
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Solving for electric field gives
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Notes that units for electric field can be volts per meter (v/m)or newtons per coulombs (N/C)
General Relation Between E and V
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It can be said that the electric field in a direction at any point is equal to the rate at which the electric potential decreases over distance in that direction
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FOr example, the electric field in the x direction over a small distance x is
Breakdown Voltage
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Breakdown -Occurs in air when electric ﬁeld exceeds about 3 ∗ 106V/m, electrons are knocked out of molecules in air
17.3 Equipotential Lines and Surfaces
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Equipotential Surface -A surface where all points are at the same potential
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An equipotential surface must be perpendicular to the electric field at any point
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The entire volume of a conductor must be entirely at the same potential in the static case, since there is no electric field in the conductor
17.4 The Electron Volt, a Unit of Energy
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Electron VOlt -Symbol is eV, unit of energy equivalent to one elementary charge moving through 1V of potential diﬀerence
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Not a proper unit, should be converted to J
17.5 Electric Potential Due to Point Charges
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Coulomb’s Potential -Electric potential at a distance from a point charge is
For a single point charge, V=0 and r=∞
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Finding the electric field due to multiple point charges, can be found by adding each electric field vectorially, all that is needed is the charge and position of each point charge
17.6 Potential Due to Electric Dipole; Dipole Moment
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Electric Dipole -Two point charges of opposite charge but equal magnitude, divided by a distance
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The potential diﬀerence at a point due to a dipole is the sum of the potentials due to each charge,
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Dipole Moment -Potential diﬀerence cause by a dipole at an arbitrary point, equal to distance between charge times magnitude of charge,
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Polar Molecules -Molecules that have a dipole moment
17.7 Capacitance
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Capacitor -A device that can store electrical charge, consisting of two conducting objects placed near each other
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Also called condensers as they condense large amounts of electrical energy
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In circuit diagrams, the symbol for capacitors is
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IN circuit diagrams, the symbol for a voltage source is
Where the larger end represents the positive end and the smaller end represents the negative
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The amount of charge held by each plate in the capacitor is calculated by
Q = CV
Where V is the potential diﬀerence bteween the plates and C is the capacitance
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Capacitance -Measured in coulombs per volt or farads
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Capacitance between two parallel plates can be calculated by
Where A is the area of the plates and d is the distance between the plates, 0 is the permittivity of free space
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Condenser Microphone -Uses a capacitor in the microphone to detect changed in air pressure
Derivation of Capacitance for Parallel Plate Capacitor
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Plugging the equation for voltage into C = givesQ V
Q
C = = (Q/A0)d
Which simplifies to
17.8 Dielectrics
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Dielectric -Materials that break don less readliy than air, usually placed between plates in a capacitor
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Dielectric Constant -Unique to various materials, this increases the capacitance of a capacitor depending on the dielectric
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Dielectric Strength -The maximum electric field before breakdown occurs
Moleculr Description of Dielectric -
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Electric field within the dielectric of a capacitor is less than it would be in air, which causes a voltage decrease
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To keep Q constant in Q = CV, capacitance must increase
17.9 Storage of Electric Energy
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The work done to move the total charge Q from one plate to another is
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Thus the potential energy stored in a capacitor is
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The potential can also be calculated as
Health Eﬀects
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Ventricular Fibrillation occurs when the heart beats fast irregular rates
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This can be solved by a defribillator which is a capacitor charged to a high voltage, which stops the heart and is normally followed by regular heart rhythm
17.10 Digital; Binary Numbers; Signal Voltage
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Supply Voltage -A constant voltage used to power devices
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Signal Voltage -A variable voltage used to aﬀect something else
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Analog -Describes signal voltages that vary continuously
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Digital -Voltages with only two possible values, on or oﬀ
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Decimal -Latin for 10
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Binary -Describes a number system where each digit or bit has two possibilities, 1 or 0
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Each place in binary increases in value by a power of 2
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Digital information is contained in a byte which contains 8 bits allowing for 28 = 256 possible values
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Analog to Digital Converter -A device that converts analog voltages to digital
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Digital to Analog Converter -A device that converts digital voltages to analog
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Quantization Error -Loss in the original analog signal by an analog to digital converter, can be mitigated by increasing bit depth and sampling rate
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Bit Depth -Number of bits for a given voltage
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Sampling Rate -Number of times per second the original signal is measured
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Digital data can be compressed in order to tak eup less storage space
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Bandwidth -Fixed range of frequencies allotted to a radio or tv station or internet connection
Noise
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Noise -Unwanted electrical signals from external sources
17.11 TV and Computer Monitors; CRTs, Flat Screens CRT
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CRT -Stands for Cathode Ray Tube, a device that depends on thermionic emission, allows for deflection of an electron beam
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The electrodes in a CRT are the cathode, or negative, and anode, or positive
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CRTs emit rays of negative charge called cathode rays but now known as electrons
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Grid -Component of CRTs that limits how many electrons can escape by producing a negative voltage
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Color Screens -May also use CRTs but each pixel has red, blue, and green phsophors that glow when hit by an electron
Flat Screens and Addressing PIxels
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Pixel -Short for picture elements, consist of 3 subpixels, one red, blue, and green, to produce a picture
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Addressing -The process of providing each pixel in a display with the correct voltage, done by providing voltage to only one row of pixels at a time
Active Matrix
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Active Matrix -Used in displays, each pixel has a thin-film transistor which can block or allow a voltage
Oscilloscopes
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Oscilloscope -A device used to amplify, measure, and display electrical signals
17.12 Electrocardiogram
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Electrocardiogram (EKG) -Used to record tha potential changes in a person’s heart
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Cells are polar, when muscle cells contract they ”depolarize” which emits a voltage
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When the heart beats the tiny voltages produced by each muscle cell add up and can be measured