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Physics 0175 study guide

by: Michael Calhoun

Physics 0175 study guide PHYS 0175

Marketplace > University of Pittsburgh > Physics 2 > PHYS 0175 > Physics 0175 study guide
Michael Calhoun
GPA 3.94

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These notes go over what's on midterm number 2, all the material since midterm 1
Phys 0175
Dr. Nero
Study Guide
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This 14 page Study Guide was uploaded by Michael Calhoun on Monday February 29, 2016. The Study Guide belongs to PHYS 0175 at University of Pittsburgh taught by Dr. Nero in Winter 2016. Since its upload, it has received 126 views. For similar materials see Phys 0175 in Physics 2 at University of Pittsburgh.


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Date Created: 02/29/16
Michael Calhoun  Physics 0175 Exam Study Guide, Midterm 2  February 28, 2016    A. Capacitors  a. Capacitor​ : A device that stores energy in an electric field  i. The larger the charge, the stronger the electric field and the larger the  potential difference  ii. Different shapes have different proportionality between ‘q’ and ‘∆V’  iii. q = CV  1. ‘C’ is a constant. Once capacitor is built, ‘C’ never changes  2. Units: Farads. 1 Farad = 1 Coulomb/Volt  iv.  Any two charged objects can  form a capacitor  v. A parallel plate capacitor is two square pieces of metal separated by a  distance with a potential difference between them.  B. Capacitors in electric circuits  a. This drawing shows the circuit symbols used to denote a capacitor, battery, and a  switch  C. Energy stored in a capacitor  ΔU dU a. ΔV = q , so dV = q   b. Since q=CV:   i. dV = dU   CV ii. dU = CV dV   U V iii.   ∫dU = V ∫V set zero for U and V at the same place  0 0 2 q2 iv. U = C2 = 2C    D. Dielectrics  a. C = K C* vacuum, ‘K’ is dielectric constant  actual b. ε = Kε , orue for any equation with ε   o c. This image shows what dielectrics do in electric fields; their internal molecules  set themselves up to counteract the original electric field. This reduces the overall  electric field, which increases the charge on each plate of a capacitor which  increases capacitance  E. Dielectrics and Capacitors  a. Dielectrics  i. Weaken electric fields  ii. Increase capacitance  iii. Case 1 shows what happens to a capacitor when a dielectric is introduced  and the voltage is constant; the capacitance increases and the charge on  the plates increases. Case 2 shows what happens when a dielectric is  introduced and the charge is constant; the capacitance increases and the  voltage decreases.  F. Calculating Capacitance  a. Steps:  i. Find the electric field  ii. Find the voltage from the electric field  q iii. Use C = V   b. For parallel plate capacitors: C = ε oA ​where ‘A’ is the area of the plates and ‘d’ is  d the distance between them.  G. Energy density of an electric field  a. Every object is a capacitor, every electric field stores energy  b. Energy per volume stored in an electric field:  U = ε E  2 V 2 o H. Spherical Capacitor  a.   b. C = 4πε o ab   b−a I. Cylindrical Capacitor  a.   L b. C = 2πε oln(b)−ln(a) J. Capacitors in parallel and series  a. n For capacitors in parallel C equivalent∑ C  iwhere ‘n’ is the number of capacitors  n i=1 1 1 b. For capacitors in series  C equivalent Ci where ‘n’ is the number of capacitors  i=1 K. Current Density / Drift Velocity    a. I = Jd∫ where J is current density    b. c. Comments:  i. Current is a scalar but is often drawn with a direction  ii. That direction is direction of positive charge flow  iii. Electrons actually move in other direction  iv. Speed of charges is drift velocity, Vd is s ​low  v. Charges move because there is a nonzero electric field because a wire is  not at equilibrium with a potential difference  d.  J = neV  wd ​ here ‘n’ is the number of charges and ‘e’ is the elementary charge  L. Resistance and Resistivity  a. Resistance: R = V   I V i. units: 1 ohm (Ω)  =  1  A ii. Resistance is constant, is a property of the object  b. Resistivity:​  ρ = J i. units: Ω *  ii. or conductivity:  σ =  units: Ω −1 m  1 ρ * iii. property of a material  iv. temperature dependent  M. Calculating resistivity of a metal  me a. ρ = ne τwhere ‘τ ’ is the average time between collisions of electrons in the  material  N. Resistance of a uniform wire  a. R = ρ  where ‘A’ is the area of the circular face of the wire  A O. Ohm’s Law  a. I = V   R b. Graphs of current versus voltage for conductors, semiconductors, and  superconductors  c. Ohm’s law doesn’t work for:  i. semiconductors  ii. superconductors  iii. conductors at very high voltage  P. Power  a. P = IV  can be used for any energy transfer in a circuit  b. Resistors  i. P = I R current through a resistor  V2 ii. P = R  voltage drop across a resistor  Q. Real batteries  a. Instead of ‘V’ they have ‘ε’, ‘electromotive force’ with same units as ‘V’  b. For ideal batteries, ε = V   c. R. Determining change in voltage  a. This is for finding the potential difference for Kirchhoff’s Laws, explained later  S. Circuit Analysis  a. ΔV  between two points in a circuit is the sum of ΔV  along any path  b. ΔV totalround any closed loop is zero  T. Grounding  a. Sets voltage to zero at the point (or points) that are grounded  b. All grounded points are connected  c. No current will flow to ground unless a complete loop through ground can be  made  U. Ammeters and Voltmeters  a. Ammeter  i. Measures current through itself  ii. Connected in series  iii. Must have very small internal resistance  b. Voltmeter  i. Measures voltage across itself  ii. Connected in parallel  iii. Must have very large internal resistance  c. Picture of ammeters and voltmeters as they would be depicted in a circuit  V. Kirchhoff’s Circuit Laws  a. Loop Rule  i. ΔV around any closed loop is zero  b. Junction Rule  i. Sum of currents into a junction equals sum of currents out of junction  c. Multiloop circuit recipe  i. Simplify resistors if possible; re­draw circuit  ii. Each branch has its own current; 1 equation per branch  iii. For 3 branches, junction rule gives one equation  iv. Use loop rule for other equations  W. RC Circuits  a. Charging a Capacitor  i.   −t ii. q(t)  =  εC(1 − e ) C ε −t iii. I(t)  =  Re  C iv. V (t)  =  ε(1 − e )  v. RC is the time constant, a smaller time constant means it takes less time  to charge. Every RC seconds the voltage increases by 63% and the  current decreases by 63%  b. Discharging a Capacitor  −t i. q(t)  =  q o  C −qo −t ii. I(t)  =  RC e , negative sign just means the current is in the opposite  direction of the charging current  iii. V (t)  =   e  Ct C X. Magnetic Fields  a. Definition of Magnetic Field  i. F b =  qv × B   ii. Magnitude: F   =  BvBsinθ​  where ‘θ’ is the smallest angle between v and  B   iii.   Y. Magnetic Poles  a. North is like a  positive electric charge, south is like a negative electric charge, but every magnet  has a north and south pole.  b. Magnetic fields are made by currents, motion of charged particles  Z. Magnetic Fields and Circular Motion  a. Since magnetic force is perpendicular to the velocity, magnetic fields cause  circular motion  b. Protons have more mass than electrons, so their paths will be much larger than  an electron’s2because the magnetic force is still the same  c. |q|vB  =   mv , centripetal force caused by a magnetic field  r AA.Charge­to­mass ratio of electron  a. A charged particle will go in a straight line if the net force is zero  i. Net force will be zero if the magnetic and electric fields are crossed and  the velocity is just right  ii. 2   iii. e  =  1 E 2  m 2 V B BB. Measuring number of charge carriers  a. electrons will pile up until the other electrons can go in a straight line  b. c. n  =   IB   V le CC. Mass spectrometer  a.   qB r b. m  =   2V   DD. Force on a wire  a.   b. F   B  IL × B where L points in the direction of the current 


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