Physics – Electricity and Magnetism - Quick Guides | Physics

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Study GuidePhysics–Electricity and Magnetism1. CapacitorsWhat is a Capacitor?Acapacitoris an electrical device used tostore electric charge.It is made oftwo or more conducting platesseparated by aninsulating materialcalled aninsulatorordielectric.When connected to a circuit, a capacitor canstore energyand thenrelease it when needed. Thismakes capacitors very useful in electronic devices.1.CapacitanceThe ability of a capacitor to store charge is calledcapacitance.Capacitance is defined as theratio of the charge stored (Q)on the plates to thepotentialdifference (V)between them:[C = Q/V]Unit of Capacitance•Capacitance is measured infarads (F)•(1coulomb/volt)2.Parallel Plate CapacitorIn the simplest type of capacitor, there aretwo parallel plates:•One plate is positively charged•The other plate is negatively charged•The plates are separated by a distance (d)For aparallel plate capacitor in a vacuum, the capacitance is:

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Study GuideWhere:•(A) = area of each plate•(d) = distance between the plates•(\varepsilon_0) = permittivity of free spaceThis formula is validonly when there is a vacuumbetween the plates.3.Effect of a DielectricWhen anon-conducting material (dielectric)is placed between the plates:•More charge can be stored•The capacitance increasesThe factor by which capacitance increases is called thedielectric constant.With a dielectric filling the space between the plates, the capacitance becomes:Values of dielectric constants are listed inmaterial property tables.4.Energy Stored in a CapacitorA charged capacitor storeselectrical energy.The energy can be calculated usingany oneof the following equivalent formulas:Each formula is useful depending on which quantities are known.

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Study Guide5.Capacitors in ParallelCapacitors are connected inparallelwhen:•Allpositive platesare connected together•Allnegative platesare connected togetherKey Points for Parallel Capacitors•Thevoltage across each capacitor is the same•Thetotal chargeis the sum of individual charges[Q = Q1+ Q2]Since (Q = CV):Cancelling (V):Rule for Parallel CapacitorsThe equivalent capacitance is thesum of the individual capacitances.

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Study Guide6.Capacitors in SeriesCapacitors are connected inserieswhen:•Thepositive plate of one capacitoris connected to thenegative plate of the nextKey Points for Series Capacitors•All capacitors carry thesame charge (Q)•Thetotal voltageis shared among the capacitorsIn series combinations, all thecapacitors have the same charge. The potential differences across thecapacitors add to equal the potential difference between the terminals of the battery; therefore,Substituting these equations into the equation for potential difference gives

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Study GuideCancelling the charge gives the following expression for the equivalent capacitance for seriescombinations:Rule for Series CapacitorsAdd thereciprocalsof the capacitances, then take thereciprocal of the final answer.2. Current andResistanceElectric circuits are everywhere around us—from mobile chargers to light bulbs at home. Tounderstand how these circuits work, we need to learn a few key ideas:current,voltage (emf),resistance, andpower. Let’s explore each one step by step.1.CurrentElectriccurrenttells us how fast electric charge is flowing through a circuit.What is current?Current (symbolI) is defined as theamount of electric charge passing through a cross-section ofa wire per unit time.In simple terms:•More charge flowing each second → larger current•Less charge flowing → smaller currentUnit of current•Current is measured inamperes (A)

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Study Guide•1 ampere = 1 coulomb per secondThis definition works for:•Charges moving in metal wires•Ions moving inliquids (electrolytic cells)•Charges moving in gases2.How fast do electrons actually move?It is tempting to imagine electrons racing around a circuit at high speed. In reality,individualelectrons move very slowly.•The average speed of electrons is called thedrift velocity•In a copper wire, this speed is about10⁻⁴ m/sThe drift velocity depends on:•The charge of an electron (q)•The cross-sectional area of the wire (A)•The number of free electrons per cubic meter (n)At this slow speed, an electron would takeabout 11 minutesto travel just10 cm!Then why does the bulb light up instantly?When the circuit is completed:•Anelectric fieldis set up throughout the wire almost immediately•Charges everywhere in the wire start moving at nearly the same time•So the bulb glows right away, even though each electron moves slowly3.Voltage, Circuits, and Current DirectionAbatteryprovides avoltage (V)between its terminals. This voltage creates an electric field in thewire, which causes charges to move.

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Study GuideWhat is a circuit?Acircuitis a complete, closed conducting path that allows current to flow from one terminal of thebattery to the other.Direction of current•By convention,current is defined as the direction positive charges would move•In metals, the actual moving charges areelectrons (negative charges)•Therefore,electrons move opposite to the direction of currentImportant note:Electric fields do not exist in conductors with stationary charges, butthey do exist when charges aremoving, allowing current to flow.4.Electromotive Force (emf)Theelectromotive force (emf)is thepotential difference between the battery terminals when nocurrent is flowing.•It is measured involts (V)•Despite the name,emf is not a force•The term is historical, but it is still commonly used in physics5.Resistance and ResistivityOhm’s LawExperiments show that, for many conductors,current is directly proportional to voltage. Thisrelationship is known asOhm’s Law:V = IR

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Study GuideWhere:•V= voltage•I= current•R= resistanceUnit of resistance•Resistance is measured inohms (Ω)•1 ohm = 1 volt / 1 ampereWhataffects resistance?The resistance of a wire depends on:1.Length (l)–longer wires have more resistance2.Cross-sectional area (A)–thicker wires have less resistance3.Material–different materials resist current differentlyThis material property is calledresistivity (ρ).•Resistivity values are found in material property tables•The unit of resistivity isohm-meter (Ωm)The relationship between resistance and resistivity is:R = ρl/AImportant distinction•Aresistoris a device made specifically to resist current•Resistancecan come from anything that opposes current, such as:○Light bulbs○Heating elements

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Study Guide6.Electrical Power and EnergyWhere to paste the imageFigure 1 shows a simple electriccircuit:•Abatterysupplies voltage (symbolε)•Wires connect the battery to alight bulb•The filament of the bulb acts as aresistor (R)Assume:•The wires have negligible resistance•The bulb is the only significant resistance in the circuitIf the battery provides6 volts:•Charges move fromhigher potential to lower potential•As current flows through the bulb,electrical energy is converted into light and heatElectrical powerPoweris the rate at which electrical energy is used or converted.Power can be calculated using any of these equivalent formulas:•P = IV

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Study Guide•P = V² / R•P = I²RUnit of power•Power is measured inwatts (W)•1 watt = 1 joule per second = 1ampere-volt3.Direct Current CircuitsIn everyday devices like flashlights and simple lamps, electric current flows inone direction only.This type of current is calleddirect current (DC)and is supplied by batteries.In this section, we study two main kinds of DC circuits:1.Circuits made using combinations of resistors2.Circuits that contain multiple batteries and more than one loopTo simplify the analysis, we assume that theconnecting wires have negligible resistance.1.Series and Parallel ResistorsEvery electrical component offers some resistance to the flow of current. This resistance may comefrom:•Light bulbs•Heating elements•Special components calledresistors, designed only to oppose current2.Resistors Connected in Series

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