I'm pretty sure these materials are like the Rosetta Stone of note taking. Thanks Briana!!!
. Other: Your study guide is just a copy/paste of the textbook. It would be ok if it weren't for the overlapping boxes which completely cut out information. Very poorly organized and almost useless
Direct Current: The current which flows through a battery in one direction.
DC circuits: consists of circuit elements including resistors and batteries or even other sources of a constant emf which is connected in closed loops
Branch Points: where three or more conductors join at points; so points C and D would be branch points.
Don't forget about the age old question of What is the difference between working memory and declarative memory?
Open circuit: This would be an incomplete loop also known as a path that is not closed. Steadystate current: zero
Short circuit: the ideal conducting path connecting across circuit element or element combination. Current is zero. These shorts can possibly cause a very
dangerous large increase through the circuit in the current.
(b) A two-loop circuit (a) A one-loop circuit
Kirchhoff’s first rule: sum of currents going in any branch point would be zero:
Kirchhoff’s second rule: sum of voltage drops near any closed path would be zero
We also discuss several other topics like What are the four crusades states?
The red wire make a short
circuit between a and b.
Series Resistors: they
connecting end to end, no
branch points are in
between, that way the
current is the same in each. The sum of the resistance is the equivalent resistance of resistors.
Equivalent Resistance the single resistor that carries the same current as the network as for the potential difference across it is the equivalent as that across the network. We also discuss several other topics like What is f-test?
Don't forget about the age old question of Where does heritable variation come from?
Parallel Resistors: connecting so potential difference will be the same across them all. Find the sum of the inverses of the resistances to find the inverse of the equivalent resistance for parallel resistors.
Ex.1 Find current I.
I3= I3 I2 = 5A10 A=15 A
Ex.2 Verify the sum of the voltage drop is zero or a counterclockwise loop
beginning at the point a.
Ex. 5 Equivalent Resistance of a Network. If you want to learn more check out Define indifference curve.
Find equivalent resistance of network
Find current through 4.0 resistor when Ω Vab = 30
If you want to learn more check out What are the four types of family?
Multiloop circuits more than one loop. Apply
Ex. 7 Currents and Voltages in a Multiloop
a.The circuit that will the measure the current in the resistor of ammeter A?
b. The effect the ammeter should have on the other circuit?
b.Find voltage of the 15 V battery, Vba
1.0 Resistor is the battery internal resistance. Ω
resistance of 10mA.
Ex. 8 Finding an Unknown Resistance by current
Kirchhoff’s rules in order to calculate currents andpotential differences in circuits.
Ammeter: measure electric current
Connected in series with adjacent circuits elements.
Ammeter should have zero resistance so current through circuit that doesn’t have the ammeter unchanged. Often smaller than 1Ω
and voltage measurements.
Ammeter has a resistance of 1 and reads current in Ω
milliamperes also known as 103A>mA. Voltmeter has
6 .show meters being use to measure Ω
current through R, while voltage dropping across R,
and the value R. Voltmeter is 11 V & ammeter is 50
Voltmeter measure potential difference. Connected in parallel with adjacent circuit elements.
Should have an infinite resistance so the equivalent resistance between points of
connection will be unchanged by the
voltmeter. Resistance most times greater than 1 MΩ
Ex.9 Charging a Capacitor in an RC Circuit
Find current when switch Is 1st closed, and the final charge is stored on the capacitor, the circuits time constant
Discharging a Capacitor
If at the beginning the capacitor is charged, we can discharge a charged capacitor by having it connected to a resistor directly across its plates.
e Exponential decay
Electric shock physiological reaction or injury that is caused by electric current that passes through the human body.
Body is sensitive to external imposed electric voltages and currents. Effects on body would depend on what the current’s magnitude, direction and the path is.
Begin to be dangerous in body by about 1mA.
Electric Shock and Electricity safety
The body’s electric resistance usually of the range of 103to 104Ω, depends on whether the skin is wet or dry. But perhaps a fatal current of 10mA can sometimes end up form a potential difference as small as 10 V.
b) ammeter in the second
diagram is short passing the resistor
a)which circuit will V measure the potential difference between points a and b?
b)what is the effect of the voltmeter in the other circuit?
b)V in 1st diagram
lowers the current
Resistance can be indirectly measured through measurements of voltage and current just as it could very well be directly measure through the ohmmeter
Multimeter can be an ammeter, voltmeter, ohmmeter, or even capacitance meter just depends
1.00*103 μF capacitor has an initial charge of .100 C. When the resistor is connecting cross the capacitor plates, there would be an initial current going through the resistor of 1.00 A. So what would the current 1.00 s later?
C=1.0 ×103μF=103×106F= 103F
I0=1.0 A I (t=15) =?
V0=Q0/C=.1 C/103100 V I0=V0/R
T=RC=(100 )(10 Ω 3)=.15
on dial setting.
RC circuit have a battery E, resistor R, capacitor
Ground connecting a point to earth b using a conductor of negligible
power where 1200
kWh of ee used in
a 30day period?
C, and switch.
resistance> potential of 0 V. grounding in an electric circuit stand for by the symbol
The Earth good conductor, carries a net negative charge on its surface of about
If originally the capacitor, C is uncharged & switch is open, to close the switch would produce a current time t:
Charging a Capacitor
the initial current
the time constant
Power Lines conducting wires maintained at some potential relative to ground
Chapter 21 Magnetism
Magnet exerts force on an object with touching not involved. Magnetic Fieldphenomen,magnetic field lines
Generate magnetic fields by permanent magnets and electric currents.
Magnetic field affect objects by magnetic force on moving charges, magnetic force and torque on electric currents, and motion of a charge in magnetic field.
Bar Magnets are attracted to metal objects.
Polesat the ends where objects are most strongly attracted (north and south)
Like repel; unlike attract
Magnetic poles not able to be isolated
Hans Oersted discovered that when a compass place close to a wire that carries an electric current, the compass needle will
Ex.1 find instantaneous
acceleration of an
electron moving at
1.0*10^7 m/s in the xy
plne, at angle 30 degrees with yaxis. A uniform
magnetic field of
magnitude 10 T is in the positive y direction.
Ex. 5 torque
Magnetic Fields, Sourcemoving charge; effect is to exert a force on other moving charge placed in the field.
Moving chargemight be isolated point charge/ electron morning through currentcarrying wire or last spinning electron the magnet
Magnetic field lines the magnetic field stands for the symbol B and characterized graphically by field lines.
Field has a nearly uniform magnitude of 0.50 T over cylindrical region of diameter of 6.0 cm & bout zero elsewhere. Fund mag force on wire, carrying a current of 40 A. Wire is perp to field and passes through the center of the cylindrical region.
Electrostatics: stationary charge
distribution produces electric fields
Magnetostatics: constant currents produce magnetic fields.
Electromagnetics: timevarying charge distributions and currents produce time varying electric and magnetic fields.
Electromagnetic induction: production of an electromotive force across a conductor exposed to time varying magnetic fields. Electric field is created in around space and thus an emf and a current is induced in a conducting loop when the magnetic field changes
When a circuit carries a time varying current, this creates a time varying magnetic field in the space around the circuit which induces an emf. A self induced emf always opises a change in current due to Lenz’s law says any induced emf opposes the change in magnetic flux that would produce it.
Selfinduced emf a timevarying current in a coil produces a selfinduced emf, opposing the emf in the coil E=L(ΔI/Δt) j
Selfinductance constant L; depend on size and shape alone. Φ=LI SI unit is 1H=1Vs/A
Inductor a coil designed to have large selfinductance in circuit in which it is inserted
Ideal inductor no resistance & represented in circuits by the symbol ___________ L=μ0N2A/l [H]
Voltage drop across an inductor a timevarying current causes a voltage drop Vab=L(Δl/Δt)
Ex. 4 find selfinductance of solenoid of length 10cm, w/ 1000 turns & cross sectional area of 2.0 cm2
L=μ0N2A/l = (4pi×107 Tm?A)(1000)2(2.0×104m2)/.10 m
221 Faraday’s Law
Induction Experiments changing
magnetic field can produce a current,
primary coil is connected to a battery
secondary connected to an ammeter.
Emfactually induced by a change in the magnetic flux rather than simply by a
change in the magnetic field.
Φ θ =BAcos B = the strength of uniform magnetic field units T*m^2=Wb
Perp =0 Parallel =90 θ θ
Faraday’s law of Induction emf induced around any loop equals the negative rate of change of outward magnetic flux through the surface bounded by the loop. = Ε ϕΔ /Δt
CQ.2210 Find the sign of the voltge drop Vab across the inductor just after the switch is opened. And estimate current through resistor 10^2 s after the switch is opened.
P.2221 A solenoid with 200 turns and crosssectional area of 1.0 cm2 is 3.00 cm long. So how much current should the solenoid carry so that the flux produced by its own magnetic field is equivalent to the flux produced by earth’s magnetic field of magnitude of .500 G, directed along the solenoid’s axis.
Lenz’ Law –the induced current produces a magnetic field that opposes the change in magnetic flux that produced it Direction of induced current resulting from the e,f is found from this law. The () in Faraday’s law is included to indicte the polarity of the induced emf.
Ex. 1 The ring has a radius of 4.00 cm and a resistance of 1.00*103 . The magnetic Ω
Magnetic field exerts a force on a
θ angle between vectors v and B
F perpendicular to the plane of v and B, in the direction of extended right thumb when fingers of right hand rotate from v to B.
Max value –perpendicular =90 degrees θ Force is zero when v is parallel to B =0 θ
Ex 5 Coils of wire wrapped around rotor in several planes. Commutator & brushes allow current to pass through any coil only when coil is in position to achieve max mag torque>xurrent pass through coil only when plane of coil is about parallel to B or when mag moment vector is about perp to B. Each coil > 100 turns of wire, area of 2.00*10^2 m^2. Current > 2.00 A, magnitude is .500 T. Find the magnetic torque assume m and B are perp to each
Right Hand Rule
Direction of instantaneous force act on a (+)
214 BiotSavart Law magnetic field produced by a small wire segment of
charge is found by this rule Place right hand on thev so fingertips point in direction of v and fingers can rotate from v to B. When hand is in that positi on, extended right thumb points in force direction
length change in l carrying current I n
on right hand from the direction of the current to the direction of the vector
direction determined if you rotate fingers
locating the field point, with magnitude.
Define in terms of the magnetic force exerted on a test charge moving in the field with
B= F/ |q| v sin units: [T] θ SI unit Telsa (T)
1T=1 N/(Cm/s)= 1 N/Am Cgs unit is a Gauss (G)
1 G=104T earth’s magnetic field = .5G=5*105T
Ex. 6 a beam of electrons move at
RL Circuits – RL circuit containing a resistor R and an ideal
1.00*10^7 m/s describing a circular path in a uniform magnetic field of magnitude 1.00 10^3 T. Find direction of motion, period, radius.
212 Magnetic forces on current carrying
Wire of length l a current I in a uniform, external
magnetic field B
experiences a magnetic
force F of magnetic
Right hand rule determine direction of F.
CQ.2113A long, straight wire carries a positive current I into the page and find direction of the magnetic field at each point.
Ex.8 Find magnetic field at the center of circular loop of radius 2.00 cm, carrying a current of 10.0 A
3 r=a B=(4pi*10^7 Tm/A))(10.0A)/2(2.00*10^2 m)
Magnetic force between parallel wires/(2pi*r)
Parallel wires carry current in same direction a coil of wire wound around a cylindrical
attracting each other. Wires that carry opposing form, in shape of a helix. Produces a strong magnetic
currents would repel each other. field in alimited region of space. Outside B=0 B=μ
Ex.10 two long, straight, parallel wires 1.00 cm apart
Particle Moving in an External Magnetic Field If the particle’s velocity not perp to field, path is spiral>>helix Trajectory of a moving charge in anonuniform magnetic field High B>small r
=μ0/4pi(IΔlsin /r B=∑(ΔB)
circuit due to the electrical inertia of the inductor. I=E/R(1e1/τ) long straight wire directed perp to page and carries a current of 100 A into page. Find mag field
Find Rate of change of current in circuit, t=0 L=2.00mH and at field point 4.00 cm to right of wire. B= /2pi(l/r))= ((4pi*10^7 Tm/A)/2pi)(100A/.04 m)
Circular current loopmag field produced by a circular current loop at a point on the axis of the loop is given by: B=μ0/2(Ia2/r3) or B=μ0/2pi(m/r3) Ex.8 Find magnetic field at the center of circular loop of radius 2.00 cm, carrying a current of 10.0 A
3 r=a B=(4pi*10^7 Tm/A)) (10.0A)/2(2.00*10^2 m)
215 Electron Spin
field is increasing at a constant rte from .200 T to 400 Tin a time interval of 1.00*!02s. Find the current in ring.
Motional emfemf induced by the motion of a conductor through a magnetic field. |E|=Blv Ex. 2left side of the Ushaped conductor has resistance of .10 ohms and that there is
negligible resistance in each of the other three sides of the loop which includes the rod, that has a length of 10 cm nd moves at a constant speed of 4.0 m/s through a magnetic field of
Ex. 5. A very large coil selfinductance of 2.0 H and resistance of 10 ohms. 12 V battery t=0, Find the steady state current and find the current through the
coil at t=.50 s.
Magnetic energy density
magnetic energy per unit volume inside the inductor may be shown in therms of the field strength as um=(1/2)(B2/μ0) [J/m3]
Ex. 6 Find magnetic energy density inside a
superconducting coil that produces a magnetic field of 10.0T. um=(1/2)
Torque on a Current Loop in an External Field
A current loop in a uniform, external magnetic field experiences zero net force, but loop experiences a torque tending to align its magnetic moment which is m with
each that carry a current of 1.00 A going in same
electron has a mag moment due to
direction. Find the magnitude f the force on a 1.00 m a spin. But since the electron is charged, its spin
length of either wire…F=μ0/2pi(I1I2l/r)
produces a current and me (mag moment, produces a magnetic field at position r. B=μ0/2pi(m/r3)
Magnetization of permanent magnet is the magnet’s magnetic moment per unit volume M=m/v=N/V(me)
magnitude .50 T. Calculate the current induced in the loop.
R=.1 ohm L=10cm=.1m B=.5 T V=4.0 m/s |E|=Blv=(.50T)(.10m) (4.0m/s)=.20 V
direction of the B field.
Torque and Net torque
Τ θ =Frsin [Nm]
T=+Fd for counterclockwise
T=Fd for clockwise
213 Motion of Point Charge in a Magnetic 2 or more forces act on an object, net torque
act on the object given by
Uniform Magnetic field:
∑τ τ= 1+τ2+….
When a particle of charge q and mass m is = F1d1F2d2
calculated into a uniform magnetic field B Loop experience a torque tending to align its
with a velocity vector v perpendicular to the magnetic moment m with direction of B
field, F=|q|vBsin 90°=|q|vB
field =mB sin angle between m and τ α αa=F/m=|q|vB/m=v2/r centripetal
the charge will move along a circular path of radius r and period T
Ex. 13 The max magnetization of iron is 1.7*106A/m. Calculate the number of aligned electron magnetic moments per unit volume of the iron.
Magnets and Solenoids
Electric Genertors Rotating a coil of wire in an external magnetic field at an angular velocity w results in an induced emf E and a terminal potential difference Vab
223 Resistor and an AC source
i=V/R=Isinwt the current and voltage are in phase
Power loss in a resistor Pav=I2rmsR
Capacitor and an AC source i=Δq/Δt=Icos wt I=wCV i=I sin (wt ) ϕ
Magnetic field of cylindrical permanent magnet w? a uniform M along its axis is the same as that of a tightly wound solenoid with same dimensions as the magnet if
Ex.3 An electric generator operating at 60.0 Hz has a coil consisting of 100 turns enclosing an area of 5.00 m2 in a magnetic field of .100 T. (a) Calculate
ohm’s law: I=V/Xc
the product of the solenoid’s turns per unit length n
and current equals M.
Electromagnetan iron core is often placed inside a
solenoid to enhance its magnetic field. Total magnetic
field –sum up the fields produced by soleoid current by
iron;core produces a strong resultant field.
2153 metal rod of length 20.0 cm and mass 100 g is
free to slide over two parallel, horizontal metallic rails
connected to a 10.0 V batter. Internal resitance of .100
and rod and rails have neglible resistance. A 2.00 T
the maximum value of the emf generated.and find
A vertical magnetic field of 2.00×102T, a ring of max instantaneous power supplied by the generator
radius 1.00 cm is flipped in the air as one would when the current is 50.0 A.
flip a coin, so that it begins rotating about a E0=NBAw=(100)(.100T)(5.00m2)(2pi×60.0Hz)
horizontal axis at a rate of 50.0 rev/s. find max =18800V
instantaneous emf induced in the ring and max P=IE0=(50.0A)(18800V)=940000
current if the ring has W=940kW=.940MW
Inductor and an AC Source V=Vsinwt
i=Issin(wt ) ϕ
inductive reactance: XL=wLohms
of a 60.H
Find rms current that resuts from connecting a 2.00muF capacitor directly across a 120 Vrms source at a frequency
Find reactance of 2.00mH inductor at a frequency 60.0 Hz