Physics 2 Exam 2

Amount of charge a capacitor can store depends on

voltage applied and capacitor’s physical characteristics, like size

Capacitance

C = Q/V, C = e0(A/d)

At constant Q or V

increasing distance decreases capacitance

Total capacitance in series

1/Cs = 1/C1 + 1/C2 + 1/C3…

Total capacitance in parallel

Cs = C1 + C2 + C3…

Energy stored in capacitor

Ecap = ½(QV) = ½CV^2 = Q^2/2C

Current

rate at which charge flows, I = ΔQ/Δt (A)

Direction of current

direction positive charge moves

Current equation (w/ drift velocity)

I = nqAvd, where A = cross-sectional area of wire, n = free-charge density of wire material, q = charge of each carrier, vd = drift velocity

Ohm’s law

V = IR

Resistance given cylinder length and area

R = pL/A, where p = resistivity of material, L = length, A = cross-sectional area of wire

Higher temperature

higher resistivity in metals (bc metal atoms vibrate more), lower resistivity in semiconductors/insulators (bc more charge carriers)

Electrical power

rate that energy is supplied by a source or dissipated by a device

Power equations

P = IV = V^2/R = I^2R

Total resistance in series

Rs = R1 + R2 + R3…

Total resistance in parallel

1/Rs = 1/R1 + 1/R2 + 1/R3…

Resistors in series - current

each resistor in a series circuit has the same amount of current flowing through it

Resistors in series - voltage/power

voltage drop/power dissipation across each individual resistor in series is different, combined total adds up to power source input

Resistors in parallel - current

current flowing through each resistor in a parallel circuit is different, depending on the resistance

Resistors in parallel - voltage/power

each resistor in a parallel circuit has the same full voltage of the source applied to it.

EMF

potential difference of a source when no current is flowing

Voltage output of a device - terminal voltage V

V = emf - Ir, where r = internal resistance of a voltage source

Multiple voltage sources in series

internal resistances add, emfs add algebraically

Kirchhoff’s junction rule

the sum of all currents entering a junction must equal the sum of all currents leaving the junction

Kirchhoff’s loop rule

the algebraic sum of changes in potential around any closed circuit path (loop) must be zero

Voltmeter

placed in parallel with voltage source to receive full voltage, must have large resistance to limit its effect on circuit

Ammeter

placed in series to get full current flowing through a branch, must have small resistance to limit its effect on circuit

RC circuit

has both a resistor and capacitor

Time constant RC circuit

τ = RC

Magnetic force exerted by field on moving charge q

F = qvBsinθ, where θ is the angle between the directions of v and B

RHR1 - direction of force on moving charge

thumb toward v, fingers toward B, palm points toward F

Magnetic force can supply centripetal force and cause a charged particle to move in a circular path of radius

r = mv/qB, where v is the component of the velocity perpendicular to B for a charged particle with mass m and charge q

Magnetic force on a current-carrying conductor

F = ILBsinθ, where I = current, L = length of a straight conductor in a uniform magnetic field B, θ = angle between I and B

RHR2

thumb toward I, fingers toward B, palm points toward F

Torque on a current-carrying loop of any shape in a uniform magnetic field

τ = NIABsinθ, where N = number of turns, I = current, A = the area of loop, B = magnetic field strength, and θ = angle between the perpendicular to the loop and the magnetic field

Strength of magnetic field created by current in a long straight wire

B = u0I/2𝜋r, where r = shortest distance to wire

RHR3 - direction of magnetic field created by long straight wire

thumb in direction of current, fingers curl in direction of magnetic field loops created by it

Magnetic field strength at the center of a circular loop

B = u0I/2R, where R = radius of loop

Magnetic field strength inside a solenoid

B = u0nI, where n = number of loops per unit length of the solenoid

Force between 2 parallel currents (I1 and I2) separated by distance r

F/l = u0I1I2/2𝜋r, where l = unit length

Force is ___ if the currents are in the same direction, ___ if they are in opposite directions

attractive, repulsive

Dielectric

becomes polarized → produces an internal electric field that opposes the main field, increasing capacitance, reducing the voltage between the plates for a given charge (if Q constant), less energy stored in capacitor (if Q constant)

Resistance depends on

material and geometry of device/wire

Smaller cross sectional area (vdrift)

higher drift speed

Capacitor connected to battery

voltage stays the same - doubling separation halves capacitance, energy stored halves, charge decreases (electric field strength decreases

Battery not connected to battery

charge q stays the same, doubling d halves C, V doubles, energy stored doubles (doing work against plate attraction to separate them → extra energy in electric field)

Ideal wire

no resistance or internal electric field, uniform potential

Batteries in series

add voltages

Batteries in parallel

same voltage

Lightbulbs in series

brightness decreases as more bulbs added, higher resistance = brighter (voltage decreases for each because total resistance increases → total current decreases)

Lightbulbs in parallel

brightness stays the same as more bulbs added, lower resistance = brighter (same voltage)

Magnetic field lines outside magnet

point away from north pole, toward south pole

Magnetic field lines inside magnet

point from south pole to north pole

Charged particle moves parallel or antiparallel to direction of magnetic field

no magnetic force

Net magnetic force on a closed current-carrying loop if the magnetic field is uniform

net force = 0

Battery, resistory, and initially uncharged capacitor (RC circuit) are connected in series → switch closed. What happens over time?

at first, capacitor is uncharged (0 V), max current → over time, charge builds up on capacitor plates so current decreases → current eventually becomes 0 when capacitor is fully charged (exponential change), capacitor is storing energy in electric field btwn plates

Greatest torque

plane of loop is parallel to magnetic field

Point next to wire, given current

thumb current, point fingers toward the point → fingers curl in direction of field at point

Magnet next to straight wire

magnet aligns perpendicular to wire

Magnet in uniform magnetic field

north pole attracted to direction of magnetic field, 0 net force but nonzero torque

Decrease distance where particles would land spectrometer

decrease voltage to decrease velocity, stronger magnetic field, decrease mass of particles, or increase charge of particles (r = mv/qB)

Kinetic energy gained from voltage

1/2mv^2 = qV, where V = voltage

Total current in parallel

Is = I1 + I2 + I3…. (constant in series)