UWorld Electrostatics and Circuits

Ohm’s Law (Graph)

Can be expressed as a linear relationship between the current and the inverse of resistance, with voltage equal to the slope of the line

y = mx + b or I = V (1/R) + 0

Number of Electrons on an Object Equation

Q = (n)(e)

n = Q / e

n = number of electrons, Q = Electric Charge, e = charge of an electron (-1.6 × 10^-19)

Root -6 divided by root -19 = root 12

Lorentz Force

The magnetic force exerted on a moving charge inside a magnetic field. The direction of this force is perpendicular to both the magnetic field and the velocity of the charge. F = qvB sin theta

q = charge, v = speed of charge, B = magnetic field, theta = angle between B amd v

Intensity Equation

Intensity = Power / Area = Energy / Area

Decibel Scale

Measures sound intensities relative to the threshold of normal hearing. Loudness of sounds is logarithmic so the intensity of sound increases by a factor of 10 when it is doubled.

dB = 10 log(10)(I1/I2)

so dB = 10 when when I1 is 10 times bigger than I2

so dB = 20 when when I1 is 100 times bigger than I2

so dB = 30 when when I1 is 1000 times bigger than I2

so dB = 40 when when I1 is 10000 times bigger than I2

Work

F d cos Theta

A force applied perpendicular to the direction of the displacement does zero work on the object. Cos 90 degrees is always equal to zero.

Vaporization

Liquid to Gas

Condensation

Gas to Liquid

Capacitors in Parallel

C tot = C1 + C2 + C3

Capacitors in Series

1 / C tot = 1 / C 1 + 1 / C 2 + 1 / C 3

Adding Capacitors in series:

1 / C tot = 1 / 0.1 + 1 / 0.1 = 2 / 0.1

(parallel so:) 0.1 / 2 = 0.05

Standing Sound Waves

Forms inside a pipe when the waves experience constructive interference and sound resonates in the pipe.

Pipe Open on Both Ends Equation

Wavelength = 2L

Wavelength (n) = 2L / n

n = integer and (n) = harmonic of pipe

Harmonic Frequencies of pipe open on both ends: f(n) = nv / 2L

f(n) = Hz and which f(1) Hz harmonic magnet it can evenly divide into is correct.

Frequency of Sound Wave Equation

v / wavelength

Ohm’s Law

V = IR

V = Voltage, I = Current, R = Resistance

Power Dissipation

P = IV

Current Flow is:

Equal through all elements of a circuit

I = I1 = I2 = I3

Light Bulb Brightness is proportional to:

Electric power which is the product of the current and voltage.

P1 > P2 > p3

V1 > V2 > V3

Coulomb’s Law

F(C) = k (q1)(q2) / r

F(C) = magnitude of the electrostatic force, r = distance, q = two charges, and k = 9 × 10^9 N m² / C

Vector Addition

Like charges repel and opposite charges attract. A vector that repels moves in the opposite direction from the charge and a vector that attracts move in the direction of the charge,

Electric Charges

The magnitude and direction of the attractive or repulsive forces exerted between electric charges are directly proportional to the charge of each particle but inversely proportional to the square of the distance separating the charges.

Capacitance Equation

C = Q / V

C = capacitance, Q = charge, V = voltage

Inserting dielectrics (polarizable materials) between the plates of parallel plate capacitors cause electric dipoles to form between dielectrics. These dipoles reduce the magnitude of the electric field (E) so voltage decreases and capacitance increases

C = Q / (decreased) V = Q / (decreased E)(d)

Dielectric Constant (k)

The ability of a dielectric to increase the capacitance of a parallel plate relative to the capacitance of a vacuum C(0(

C = (k)(C,0)

C = Capacitance, k = dielectric constant, C,0 = Capacitance of vacuum

Capacitance Proportionalities

Capacitance is proportional to A (area) and inverse to distance (d)

C proportional to A / d

Circuits In Series

Position electrical components on a single line for a single channel for current to flow.

Parallel Circuits

Position circuit components side by side and have multiple channels for current to flow.

Resistors In Series

The current (I) passing through each resistor is constant because charge entering a resistor in series cannot accumulate. The voltage drop results from the intrinsic resistance.

V = IR1 + IR 2+ IR(n)

For resistors in series, the voltage drop across each resistor is identical.

Resistors In Parallel

Current varies with its own unique resistance. Voltage drop is identical:

V = I1R1 = I2R2 = I(n)R(n)

For resistors in parallel, the voltage drop across each resistor is identical.

Resistance Equation (from resistivity)

R = r(L) / A

R = resistance, r = resistivity

L = length, A = Area

Resistors

Electrical components that oppose the movement of charge/current and deplete electrical potential energy (voltage). The ability of a resistor to resist current is resistance (R) which is an extensive property (related to physical dimensions).

When replacing a resistor by an equivalent resistor:

Multiply the first equation by a ratio of the new resistor (Re / /Re) (Rd / Rd)

Placing multiple resistors in series:

Increases the total resistance

Placing multiple resistors in parallel:

Decreases the total resistance

Conductivity

An intensive property that describes the ease at which charges flow. Conductivity is inverse to resistivity. The conductivity of metals is attributed to loosely associated valence electrons within a metal whereas conductivity of electrolytic solutions is proportional to molar concentration of ions.

Resistivity is proportional to:

Resistance

Terminal Voltage

Electromotive force is an electrical potential gradient within the battery that produces terminal voltage that affects (resistors, capacitors, conductors)

Ideal Battery: V = E

Real Battery

V(loss) = IR

V = E - V(loss) = E - IR

V = terminal voltage, E = electromotive force, I - current, R = resistance (internal)

Electric Circuit

In an electric circuit, a source of voltage generates a current which is the flow of charges in a conductor.

Kirchhoff’s Junction Rule

At a junction (where current splits or joins together), the sum of current flow entering the junction is equal to the sum of current leaving junction.

I(enter) = I(exit)

Power Equation

P = IV

Ohm’s Law: V = IR

Can be substituted so P = V² / R

Parallel Circuit (Power Dissipation)

In a parallel circuit, the branch with the lowest resistance has the largest current and the largest power dissipation.

Series Circuit

In a series circuit the same current flows through each element.

I = I(f)

Conservation of Energy

The voltage rise from the voltage source V(s) is equal to the sum of the voltage drops across the other elements in the circuit, the resistor V(R) and the V(f)

V(R) = V(s) + V(f)

R = V(s) - V(f) / I(f)

V(s) = source voltage, V9f) = forward voltage

Frequency Equation

Frequency = speed of light / wavelength

Energy Equation

E = hf

h = plank’s constant and f = frequency

can be substituted so E = (h)(speed of light)/wavelength

Light Wavelength

Wavelength increases from purple (400 nm) to blue green yellow and then red (750 nm)

Wave Interference

When two waves at the same point they overlap with one another and cause wave interference.

Constructive Interference

Occurs when the peaks and troughs of the two waves overlap exactly, meaning the phase difference between the waves are 0 degrees. This corresponds to a path length difference of 0 degrees. This means the path length difference of the two waves ate integer multiples of the wavelength.
Delta d = 0, 1, 2, or 3

Destructive Interference

When the peaks of one wave overlap with the troughs of the other wave, the phase difference between the waves is 180 degrees. This happens when the difference in path length is half the wavelength or an odd multiple of half the wavelength.

delta d = wavelength / 2, 3 wavelength / 2

Velocity Equation

Delta x / Delta t

x = distance t = time

Frequency Equation

f = 1 / T

T = period

On a graph the peak of the wavelength is 1.5 of the y axis

Visible Light Spectrum

The visible light spectrum includes wavelengths from 400nm to 750nm

Lorentz Force Equation

F = qvB

q = charge, v = speed, B = magnetic field, F = Lorentz Force

The direction of the Lorentz force is:

Perpendicular to the particle’s velocity

Because an electron is much smaller than a proton:

An electron’s path in comparison to a positive charge would be more curved in the same magnetic field.

Conservation of Charge

In an electric circuit, when circuits are in series, conservation of charge dictates that the current through all elements in series is equal.

I(1) = I(2) = I(n)

Resistors in Parallel (Ohm’s Law)

When resistors are arranged in a parallel, Ohm’s Law implies the branch with the greater resistance has the lower current.

Conductivity Equation

C = 1 / Resistivity

Conductivity is inverse to resistivity. Both are intrinsic properties.

Modifying the physical dimensions of an electric conductor:

may influence the rate at which current flows through the conductor.

Coulomb’s Force

Electrostatic Force is proportional to (Q,1)(Q,2) / r²

Q = charge

r = separation distance

Increasing the charge on one object increases the electrostatic force on the other object

Electric Field Lines

Electric Field Lines point outward from positive charges and toward negative charges.

Electric Field Equation

The magnitude of a uniform electric field is its voltage divided by distance. SI units are (N/C) and (V/m)

E = Delta V / d

Force Exerted on a particle in Uniform Electric Field

F = qE

q = charge, E = Electric Field

Charge of Doubly Ionized Particle

Twice the charge of an electron . (1.6 × 10^-19)

Lorentz Force

F = qvB

q = charge, v = velocty, B = magnetic field

Lorentz Force for a particle with a Electric FIeld

F = q(E + (v)(B))

The force exerted on a moving charge due to a magnetic field is:

Perpendicular to both the ion’s velocity and the direction of the magnetic field.

Closed System

Only heat can be exchanged with the surroundings in a closed. The total charge in a closed system must remain constant. Net charge of the system is always zero.

Conservation of Electric Charge

Electric charge cannot be created or destroyed, The total charge is conserved in any process

Circuit Junctions

Points where three or more elements meet. By Kirchhoff’s Law, the sum of the currents entering a junction equal the

Resistance of a Resistor Equation

R = (resistivity)(L) / A

Net Vertical Force Equation

Net Vertical Force = Electrostatic Force - Gravitational Force = 0

Electrostatic Force must push upward so Net Vertical Force is Zero

Energy Stored in a Capacitor Equation

U = ½ C V²

U = Energy Stored, C = Capacitance, V = Voltage

Voltmeter

Measures the voltage between two points in an electric circuit. To measure V across a resistor, the voltmeter is connected in parallel with the resistor because circuit elements connected in parallel have the same V. The voltmeter should behave as an open circuit (have a very large resistance) for accurate measurements.

Electric Field Equation

E = kq / r²

E = Electric field, k = Coulomb’s constant, q = charge, r = distance

Heat Energy

Heat Energy is proportional to P = IV = V² / R

Distance Travelled Equation

Distance = vt

V = Speed T = Time

Electrostatic Force

Electrostatic force is conservative; the sum of potential and kinetic energy is constant. Therefore, the potential energy of a particle is the difference between the total energy and the kinetic energy.

Coulomb’s Force

F(E) = k (q1)(q2) / r²

k Coulomb’s constant, r = distance, q = charges

F(E) = Electrostatic Force

If F,e is greater than the force of gravity, one of the objects could move toward the other instead of falling to the ground.

Kirchoff’s Loop Rule

The sum of the voltage drops V around any closed loop in a circuit is zero.

V(i) = V(1) + V(2) = 0

Junction Rule (I)

Parallel Circuits can be added together to find total current

Voltage Drop

V Battery - V(1) - V(3) = 0

V battery = Voltage given from circuit

V(1) = (V = I(1)R(1) ) Rule

I(1) = Total amperes from resistors

Do algebra to get V(3) alone to find voltage drop of resistor 3

Electrical Conductors

Facilitate electrical current (the movement of charge). Mechanisms for thermal and electrical conduction are not the same but an electrical conductor can be a thermal conductor.

Electrical Inuslators

Inhibit current.

Capacitor

A device that stores electrical charge between equal but oppositely charged plates by a fixed distance. Capacitance

(C = Q/V) is measured in Faradays

Dielectric

A dielectric can be introduced between the plates of a parallel plate capacitor to cause an increase in capacitance. The dielectric (k) measures the ability of dielectric material to increase capacitance.

C = (k)(C0)

C = Capacitance with dielectric

k = Dielectric Constant

C0 = Capacitance of a vacuum

Kirchhoffs Junction Rule

Charge must be conserved when currents split or join at junctions. Total current entering a junction must equal the sum of each individual current leaving the junction.

Energy Stored in a Charged Capacitor Equation

U = ½ CV^2

U = Energy Stored C = Capacitance V = Voltage

Circuit Components in Parallel Are:

Connected to each other at both ends and have the same voltage

V = V so IR = IR

Electric Power Equation

P = IV = I²R = V²/R

Electric Charge Equation

Q = (I)(t)

Q = charge, I = current, t = time

Voltage

The difference in electrical potential between two points and drives the movement of electrical charges.

An ammeter in series with a circuit component:

measures the current through that compartment.

Because current is inversely proportional to resistance if the voltage is fixed:

Reducing the resistance in half will double the current and vice versea.

Resistivity is proportional to:

Resistance (V/I). Resistivity is an intrinsic property and varies with the changes in material’s temperature. Resistivity is represented by an exponential exponential of a voltage verse current graph.

Electric Current Equations

I = Q/T = V/R = P/V

Watt/second, Volt.Ohm, Watt/Volt

Electrostatic Force

Electrostatic force is conservative.

E initial = E final

PE initial + KE initial = PE final + KE final

PE final = E final - KE final

If Ke is doubled it is doubled twice because it is ½ mv²

Separation Distance (R)

r can be found by the pythagorean theorem

r² = (distance given)² + (distance given)²

Coulomb’s Law = K q1 q2 / r² (solved)

Poiseuille’s Law

Determines the blood flow rate. Describes the laminar flow of a viscous, incompressible fluid through a pipe. The viscosity of a fluid measures the internal friction force that resists flow.

Q = Delta P / R = pi r^4 Delta P / 8 n L

Flow rate is directly proportional to vessel radius and pressure difference but inverse to viscosity and vessel length.

Poiseuille’s Law (Units)

8 n L Delta P / pi r^4 Q

n = Delta P r / Q

n = Pa m^4 / m³ (m/s)

= (Pa)(s)

The vessel with the biggest +- change in pressure:

Has the greatest pressure difference and therefore the greatest resistance to flow.

Confounding Variable

An uncontrolled variable different from the independent variable that has an impact on the dependent variable. The effect of a confounding variable can be observed by including a group in an experiment that differs at the confounding variable.