Exam 3: Electricity and Magnetism

Electric charge

• Charge is quantized as a multiple of the electron or proton charge

  • Unit of charge is the ——

  • 1 C = 6.24×10¹⁸ e

  • 1e = 1.602×10^-19 C= 1 proton

coulomb

Electric Properties of Materials

• Different materials behave differently in the presence of electrostatic forces - 3 basic types

  • Conductors

    • Contain charges that are —- to move

    • Electrons are —- bound to atoms

    • Charge can —— — through conductors

    • Metals: copper, silver, iron, gold

  • Insulators

    • Contain charges that are —— free to move, they can only change —-

    • Electrons are —— bound to atoms

    • Plastic, ceramic, wood

  • Semiconductors

    • Are —— between good conductor and good insulator

    • Computer chips and solar panels (silicon)

free, weakly, readily flow

not, direction strongly

intermediates

Coulomb’s Law

• The influence of charges is characterized by the —— between them

• The electrostatic force (F_E) between two charged objects is ——- to the quantity of charges (q1 and q2), and —— —— to the square of the distance (r ) between the charges

  • Results in the equation: ———-

  • Where k is the Coulomb’s constant

Direction of Electrostatic Force

• The force is along the line connecting the charges

  • It is attractive if the charges are ——— and repulsive if they are the ——

forces, proportional, inversely proportional, Fe = kq1q2/r²

opposite, same

Four Fundamental Forces

• Strong force

  • Force that holds nucleus together

• Electromagnetic force

  • the —- and —— of charged particles

• Weak force

  • Neutrino interaction induces beta decay

• Gravitational force

  • gravitational attraction of masses

attraction repulsion

Analogy Between Gravitational and Electrostatic Forces

• The equations for F_g and F_e are similar in their setup

  • F_g = Gm1m2/r²

  • F_E = kq1q2/r²

• Differences

  • Gravitational force depends on the —- while electrostatic force relies on the ——-

  • Gravity is always ——- because their is no such thing as negative mass, but charges can be negative or positive so electrostatic force can be —- or ——

  • Gravitational forces are much —— than electrostatic forces

mass, charge

attractive, repulsive attractive

weaker

Electric Field

• The existence of a charge in a space creates an electric field

• The electric field describes how a charge affects the —— around it, which can exert —— on another charge in that space

  • The E at a given point is the electric force acting on a charge at that point divided by the charge: E = F_E / q (unit is N/C)

• Electric field is a ——

  • Will have the —— direction as the F_E on a positive charge placed at that point

  • Will have the —— direction as the F_E on a negative charge

• An electric field can store —— because they can do ——

space, force

vector, same opposite

energy, work

Direction of Electric Field Lines

• Convention

  • Positive charge: the vector E moves —— from the charge, so the electric field lines created by a positive charge are directed radially ——

  • Negative charge: the vector E moves —— the charge, so the electric field lines created by a negative charge are directed ——

• Electric field lines point away from —— charges and terminate on —— charges

• Electric field lines will NEVER —— each other unless E = ——

away, outward

toward, inward

positive, negative

cross, 0

An Electric Field can do Work

• If a charge is in an electrostatic field (q and E)….

• A —— exists on the charge (F_E = Eq) …

• The charge will be moved a ——- due to the force (d →) ….

• So —— is done by the electric field (W = Fd → qEd)

force, distance, work

Electric Potential

• Electric potential (voltage, U) is related to electrostatic PE, but they are NOT the same

  • Charges create field/potential and feel force/potential

• Unit is Volt

  • A unit of electric potential is unit of —— per unit of ——-

  • 1 V = 1 J/C = Energy/q = W/q = Fd/q = Ed

  • V = q / r

• Equipotential lines

  • A line at which the potential/voltage is the ——-

  • In a constant electric field they are —— spaced (parallel plate)

  • In a point charge they are —- -spaced and form ——

    • Show mirror ——- about the center point

    • They are everywhere that is —- to the electric field lines

energy charge

same

evenly, unevenly circules, symmetry, perpendicular

Electric Dipole

• A pair of equal charges of —— signs, separated by a very —— distance

• Nature likes to make dipoles

• Dipoles create, feel, and align with —— ——

• Water is a dipole molecule, that is why it’s wet

opposite short

electric fields

Capacitor

• Electric fields store electric energy, and capacitors are a device that —- electric energy

• Two metal plates and an insulator between them produce a —— electric field between the plates

  • A charge placed in the uniform electric field will experience an electrostatic force in the direction of the electric field

stores, uniform

Electrostatics Summary

• There are two types of electric charges: positive and negative

  • They have the same —— of charge

  • Like charges —- and opposite charges ——

• Coulomb’s Law is analogous to the universal gravitational law of Newton

  • Gravitational forces are only ——-

  • Electrostatic forces can be —— or ———

• Electric charge creates an —— —— that can do —— by exerting a —- over a ——

• A potential difference creates ——

magnitude, repel, attract

attractive, repulsive attractive

electric field, work force distance

voltage

Voltage (U)

• The change in potential that is meaningful and easily measurable

  • A difference in potential

  • 1 Volt corresponds to the ——- done by an external force in moving a charge of 1 C by a distance of 1 m so 1 V = 1 J/C

• PE vs Potential Difference

  • The PE of a positive charge increases when we move it ——- the field (moving in opposite direction as it naturally wants to requires work = PE)

  • The electrical potential/voltage of a positive charge increases as we move ——- to the charge (V = q / r, so decreasing r will increase V)

work

against

closer

Electric Current (I)

• The motion of —- ——

  • In a conducting wire, the moving ——- make the current

• The electric current is the time rate at which electric charges pass through a specified point in an electric conductor

  • The amount of charge that flows through the cross-sectional area of a conducting wire in a time interval

  • I = q /t

  • Unit is Ampere: 1 A = C/s

• Direction

  • Although electrons are responsible for the flow of electric current in conductors, it is the convention to take the direction of the current as if it were the positive charges which are moving

  • So we set the electric current’s direction as flowing from —— to ——- terminal

electric charges, electrons

positive negative

Electric Resistance (R)

• A property of a circuit element that —— the flow of a current

• The resistance of a metal wire is

  • proportional to resistivity (property of material of wire)

  • proportional to length of wire

  • inversely proportional to the area of the wire

  • dependent on temperature of material

  • R = p(L/A)

• If the resistance is constant over a wide range of voltage the material is said to be an —— material

• The resistance can be calculated as the ratio of —- to ——

  • This is Ohm’s Law: V = IR

    • R = U/I

opposes

ohmic

voltage current

Resistor

• A component of an electric circuit that is characterized by a resistance

  • Limits or regulates the flow of electric —— in a circuit and causes voltage —— (it’s called voltage drop because voltage will always drop across a resistor)

current, drops

Electric Power

• The electric power is related to the energy that is converted from the electric energy of the moving charges to some ——- form of energy (heat, mechanical, stored)

• For a resistor in DC circuit, the power (P) is given by the product of applied voltage and electric current

  • P = UI = I²R = U²/R

  • Unit is Watt: 1 W = 1VA

other

Electric, Mechanic, and Thermal Energy

• In electric circuits, the electric energy is supplied by a battery which draws its energy from the —— —— stored in the chemicals of the battery

  • The battery —— PE of electric charges as it moves positive charges towards the positive terminal and more negative charges towards the negative terminal (charging the battery = building up PE)

  • When we provide an external conducting path from the positive to the negative terminal, charge flows from points of —— to —— PE (connected to the circuit)

• As PE is lost, KE is gained by the —— flowing through the circuit

  • A portion of this KE is converted to heat by collisions with other electrons and atoms

potential energy

increases

higher lower

electrons

Electric Circuits Part1 Summary

• A battery is a source of constant —— —— (—-)

• Electric current is the rate of flow of —— —— over time moving from a —— to a —— terminal (in the direction that —- charge would flow)

• Resistance can be measured/calculated as the ratio of —— to —— (Ohm’s Law)

• Resistance is determined by geometry and material properties (R = pL/A)

• Electric power is the conversion of electric energy from a moving point to some —- form of energy, and is the product of —- and ——

potential difference voltage

electric charge positive negative, positive

voltage current

other, voltage current

DC and AC Current

• DC = Direct current

  • Is —- changing in time

  • The current flows in a —— direction from the positive to negative terminal

  • A battery provides steady voltage that is a source for a steady electric current

• AC = alternating current

  • Is —- in time

  • Continually —— its direction

  • An electrical socket provides changing in time voltage that is a source for an alternating current

  • AC electromotive force/voltage is produced in power plants and sent to homes

not, single

changing, reverses

Series Circuits

• In a series circuit there are no branch points into secondary loops

  • All elements line up in a —— loop

  • The —— current passes through all elements/resistors

  • Voltage ——/—— as is passes through resistors based on Ohm’s Law

  • The total voltage decrease/drop across the combination is the sum of these individual changes

  • The electromotive force is mathematically equivalent to the voltage

    • e = V_battery = V1 + V2

• Important Summary

  • Current is —— through each resistor because there are no alternative paths

    • I_Total = I₁ = I₂ = I₃ …

  • Voltage is ——- across components, where the total voltage of the battery is equal to the sum of voltage drops across the resistors in the circuit (larger resistance = larger voltage drop)

    • V_{battery =} V_{1 +} V₂ + V₃ …

  • R_eq = R₁ + R₂ + R₃ …

    • The equivalent resistance is always —— than the largest in the serial combination

single, same, decreases drops

constant

divided

larger

Parallel Circuits

• There are points at which the current can split into different paths

  • The current flow —- and then later rejoins (Kirchoff Junction Rule)

  • A —- of the total current flows through each branch, the currents can be different since they divide, but will always add to give the total current of the circuit

  • The splitting into branches —— the electric resistance for the current to flow

  • The voltage drop across each resistance is the ——-, since they are all connected between the same two points

• Important Summary

  • Voltage is —— across every branch, each get the full voltage amount from the battery

    • V_battery = V1 = V2 = V3 ….

  • Current —— between branches

    • I_Total = I1 + I2 + I3 ….

    • Lower resistance = more current passes through

  • R_eq = 1/R1+ 1/R2 + 1/R3 …

    • Or if there are only two resistors, then it’s R1R2/R1+R2

    • The equivalent resistance is always —— than the smallest in the parallel combination

divides, portion, decreases, same

constant

splits

smaller

Kirchoff’s Laws

• Junction Law

  • The sum of the electric currents entering the circuit equal the sum of the electric currents leaving the junction

  • I_In = I_Out

• Loop/Voltage Law

  • The net voltage drop around any closed loop must be ——-

  • V_battery = V_drop

  • V_battery = IR₁ + IR₂ + IR₃ ….

zero

Example Problem

• Calculate total equivalent resistance

  • First find R_{eq, parallel}

    • 1/15 + 1/30 = 1/10 = 10

  • The two parallel resistors are in series with the third so to find the total use the series Req equation

    • 10 + 12 = 22

• What is the total current?

  • Use the total Req and battery voltage to solve

  • V = IR → 6 = I(22) → I = 0.27A

• Calculate the voltage drop across R1

  • R1 is in series so its voltage drop is divided and current is constant, so use total current to calculate

  • V₁ = I_TotalR₁ → V = (12)(0.27) = 3.24

• Calculate the voltage drop from point A to B (across parallel branch)

  • From point A to B is a parallel branch, so voltage will be equal between the two branches. Since we know that for a series circuit V_battery = ∑V_drop we can say:

    • V_battery = V1 + V_parallel → 6 = 3.24 + V_parallel → 6-3.24 = 2.76

    • This is the voltage across both parallel branches, they are equal

• What is the current flowing through R2

  • R2 is in parallel so the current is divided, but the voltage is constant. We know the voltage drop from the previous question

  • V = IR → 2.76 = I(15) = 0.184A

• What is the current flowing through R3

  • Same process as above

  • V = IR → 2.76 = I(30) = 0.092A

• Calculate the power dissipated across R2

  • P = VI = I²R = V²/R

  • 2.76²/30 = 0.25 W

• What is the total power

  • V_Total x I_Total = P_Total

  • 6 × 0.27 = 1.62 W

ok

Household circuits

• Are wired in —— so that different appliances can be added or removed from the circuit without affecting the voltage available

  • As you add more appliances, the total current drawn increases because the total effective resistance of the circuit decreases when resistances are added in parallel

    • Equal voltage drops to each resistor in parallel circuits

  • Current that is too large causes the wires to overheat and cause a fire, so a fuse/circuit breaker in series will disrupt the circuit if the current gets too large

    • Fuse/circuit breaker prevents fires

parallel

Battery Packs

• Arranged in parallel provides the —- voltage but a —— current

• Arranged in series provides a —— voltage but the —— current

same, larger

higher same

Voltmeter

• Measures the voltage difference between two points in a circuit

  • Is inserted in —— with the element whose voltage difference is being measured

  • Should have a —- resistance so that is does not divert much current from the component whose voltage is being measured… we need some current flowing through the voltmeter for it to work

Ammeter

• Measures the electric current flowing through a point in a circuit

  • In inserted in —— to the circuit being measured so that all the current flows through it

  • Should have a —- resistance so that its effect on the current is small and the voltage drop across the ammeter is minimal

  • If placed in parallel it can burn out the ammeter

parallel, large

series small

Capacitors

• Ability to store charge per unit voltage

  • C = q/V

  • Unit is Farad: 1 F = 1 C/V

• Has ability to —— and —— energy

• Geometry of a parallel plate capacitor affects its ability to store charge

  • C = eA/d

• DC does —- flow through, but AC —— flow through

  • Capacitors have insulators between the two plates, so DC currents will have a break in circuit = current stops flowing

  • AC currents “flow through” capacitors, but not through the insulators, but since the direction of flow is constantly reversing the pole charge of the capacitor is changing making it seem like it’s flowing through it

    • Constant change of + and - poles of capacitor make it appear to flow

• Capacitance

  • Series: 1/C_Total = 1/C1 + 1/C2 + 1/C3

  • Parallel: C_Total = C1 + C2 + C3

store release

not, does

DC Circuits Summary

• A combination of a circuit elements (batteries, resistors, capacitors, solenoids) can be reduced to their series and/or parallel combinations

• In a series combination:

  • The electric current flowing through each resistor is the ——

  • The equivalent resistance is always —— than the greatest out of all individual resistances

• In a parallel combination:

  • The voltage across each resistor is the ——

  • The equivalent resistance is always —— than the smallest out of all individual resistances

• The total electromotive force of batteries connected in series is the —- of all electromotive forces of the connected batteries

  • Basically saying in series: V_battery = V1 + V2 + V3

• Batteries connected in parallel provide the —— electromotive force as one battery, but the electric current drawn is the sum of all currents drawn from individual batteries

  • Basically saying in parallel: V_battery = V1 = V2 = V3

• Ammeters have —- internal resistance and must be connected in ——

• Voltmeters have —— internal resistance and must be connected in —-

same, greater

same, smaller

sum

same

low, series

high parallel