phys 222 si exam review
DESCRIPTION
PHYS 222 SI Exam Review. What to do to prepare. Review all clicker questions, but more importantly know WHY Review quizzes Make sure you know what all the equations do, and when to use them. These equations are used exclusively in LRC circuits - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/1.jpg)
PHYS 222 SI Exam Review
![Page 2: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/2.jpg)
What to do to prepare
• Review all clicker questions, but more importantly know WHY
• Review quizzes
• Make sure you know what all the equations do, and when to use them
![Page 3: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/3.jpg)
• These equations are used exclusively in LRC circuits
• These equations are what let you find the major constants that do not change with time.
• Remember, capital letters are not time dependent.
![Page 4: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/4.jpg)
𝑉 𝑟𝑚𝑠=𝑉√2, 𝐼 𝑟𝑚𝑠=
𝐼√2
• These equations are used to determine the root-mean square voltage and current in an LRC circuit
![Page 5: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/5.jpg)
𝑖=𝐼 𝑐𝑜𝑠𝜔𝑡• These two equations assume that the current
in an LRC circuit is a maximum at t=0.• These equations tell the voltage and current
as a function of time.• To find remember to add the appropriate
phase constants to the cos term.
![Page 6: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/6.jpg)
𝐼 𝑟𝑎𝑣=2𝜋 𝐼
• Not mentioned in class really
![Page 7: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/7.jpg)
AC Current section on the Equation Sheet
• All the capitalized letters do not change with time.
• For example…none of these change with time:– V, I,
• To find the time dependent voltage and current, multiply by the appropriate time dependent equation.
![Page 8: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/8.jpg)
How to determine v(t), i(t),
• The current phasor is parallel with the phasor.• leads , and lags • The voltage – I.E. if then
![Page 9: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/9.jpg)
What happens to a circuit at resonant frequency?
• The voltage phasor is parallel with the current phasor (this does not usually happen)
• (recall that both do not depend on time)• The sum of the voltages across the inductor
and the capacitor equals 0.
![Page 10: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/10.jpg)
Example #1
• At t=0, the current in the circuit is a maximum of 3 A.
• Then…
• Also note that without doing any math you know that and – Make sure you understand why.
![Page 11: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/11.jpg)
Example #2
• Let’s say that in an LRC circuit,
• Also suppose that you’ve calculated the phase angle to be, and
• Then
![Page 12: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/12.jpg)
Example #3
• They tell you
• To calculate I, find Z, then use • To calculate , first find I, then use
• Finally, if you need time dependence, add the appropriate phase shift to the cos or sin.
![Page 13: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/13.jpg)
![Page 14: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/14.jpg)
𝑝=𝑖𝑣• Equation relating power, current, and voltage
![Page 15: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/15.jpg)
𝑃𝑎𝑣𝑒𝑟𝑎𝑔𝑒=12 𝐼𝑉𝑐𝑜𝑠𝜙=𝐼 𝑟𝑚𝑠𝑉 𝑟𝑚𝑠𝑐𝑜𝑠𝜙=𝐼 𝑟𝑚𝑠2 𝑅
• Average power in an LRC AC circuit
![Page 16: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/16.jpg)
𝑉 2
𝑉 1=𝑁 2
𝑁 1
• Equations used to convert a voltage inside a transformer
![Page 17: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/17.jpg)
𝑉 1 𝐼 1=𝑉 2 𝐼2• Current and voltage in a transformer
![Page 18: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/18.jpg)
𝐸 (𝑥 , 𝑡 )=𝐸𝑚𝑎𝑥 cos (𝑘𝑥−𝜔𝑡 ) �̂�• The equations for electromagnetic radiation,
or in other words light• Note that the direction of propagation is +x.• Also note that
![Page 19: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/19.jpg)
𝑐=1
√𝜖0𝜇0• Speed of light related to two constants
![Page 20: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/20.jpg)
𝑢=12𝜖0𝐸2+
12𝜇0
𝐵2=𝜖0𝐸2=𝐵2𝜇0
• Energy density
![Page 21: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/21.jpg)
𝑃=𝐹𝐴=
1𝐴𝑑𝑝𝑑𝑡 =
𝑆𝑐=
𝐸𝐵𝜇0𝑐
• Equations relating the radiation pressure of an electromagnetic wave to the poynting vector and E and B.
![Page 22: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/22.jpg)
𝑺=1𝜇0
𝑬×𝑩
• Poynting vector.• Note that the poynting vector is perpendicular
to both E and B
![Page 23: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/23.jpg)
𝐼=𝑆𝑎𝑣𝑒𝑟𝑎𝑔𝑒=𝐸𝑚𝑎𝑥𝐵𝑚𝑎𝑥
2𝜇0=𝐸𝑚𝑎𝑥2
2𝑐𝜇0=12 √ 𝜖0𝜇0 𝐸𝑚𝑎𝑥
2 =12𝜖0𝑐 𝐸𝑚𝑎𝑥
2
• The intensity of electromagnetic radiation, related to the E field.
![Page 24: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/24.jpg)
• Equations relating the speed of light c, the wavelength of light , the frequency of light the angular frequency , and the wave number .
![Page 25: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/25.jpg)
𝑛=𝑐𝑣
• The speed of light in a medium of index of refraction .
• For example, in glass the speed of light is not equal to m/s, but instead it’s equal to m/s (
![Page 26: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/26.jpg)
𝜃𝑖=𝜃 𝑟𝑅𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛• The equations for reflection and refraction
![Page 27: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/27.jpg)
𝐼=𝐼𝑚𝑎𝑥cos (𝜙 )2
• The equation for intensity of light through a diffraction grating.
•
![Page 28: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/28.jpg)
sin (𝜃𝑐𝑟𝑖𝑡 )=𝑛2𝑛1
• The equation used to find the critical angle between two interfaces.
• At angles equal to or greater than the critical angle, refracted rays stop going through the second medium. Instead they undergo total internal reflection.
• Sometimes light coming from one direction onto an interface doesn’t have a critical angle, but if the light goes the other direction, then the critical angle exists.
![Page 29: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/29.jpg)
𝑡𝑎𝑛𝜃𝑃=𝑛2𝑛1
• Equation used to find Brewster’s Angle, also known as the Polarization Angle .
• This angle is where reflection stops happening.
![Page 30: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/30.jpg)
1𝑠 +
1𝑠′
=1𝑓
• The master equation for both lenses AND mirrors
![Page 31: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/31.jpg)
• ALWAYS…s>0. (the distance from the real object to the vertex of the mirror, or from the real object to the lens)
• For MIRRORS…– f>0 if the mirror is concave, if the mirror is convex, then
f<0. Also f=R/2.– s’>0 if the image is on the same side as the outgoing rays
• For LENSES…– f>0 if the lens is more converging, otherwise f<0 if the
lens is more diverging
![Page 32: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/32.jpg)
𝑚=𝑦 ′𝑦 =− 𝑠
′
𝑠• Magnification caused by a mirror or lens
![Page 33: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/33.jpg)
𝑓 h𝑠𝑝 𝑒𝑟𝑖𝑐𝑎𝑙𝑚𝑖𝑟𝑟𝑜𝑟=𝑅2
• Focal point of a spherical mirror
![Page 34: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/34.jpg)
1𝑓 =(𝑛−1 )( 1𝑅1 −
1𝑅2 )
• “Lensmaker’s Equation”
![Page 35: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/35.jpg)
𝑛𝑎𝑠 +
𝑛𝑏𝑠′
=𝑛𝑏−𝑛𝑎𝑅
• Look up
![Page 36: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/36.jpg)
𝑚= 𝑦 ′𝑦 =−
𝑛𝑎𝑠 ′
𝑛𝑏 𝑠
• Spherical fish bowls is the main application of this equation
![Page 37: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/37.jpg)
𝑀=𝜃′𝜃
• M is the angular magnification of a telescope.• Recall that and
![Page 38: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/38.jpg)
𝑑𝑠𝑖𝑛𝜃=𝑚 𝜆• This is the equation for two-source
interference, used to find where the bright fringes are.
• To find the dark fringes, replace m with (m+1/2)
![Page 39: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/39.jpg)
𝑑𝑠𝑖𝑛𝜃=(𝑚+ 12 )𝜆
• Destructive interference.
![Page 40: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/40.jpg)
𝑦=𝑚𝑅𝜆𝑑
• Assuming small angles the equation on the previous slide gives this result, where R is the distance between the slits and the screen, d is the separation of the slits, m is an integer, and y is the height above the central interference maximum.
![Page 41: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/41.jpg)
𝐼=𝐼𝑚𝑎𝑥cos ( 𝜃2 )2
• In single slit diffraction, you can use this equation to find the intensity as a function of the angle.
![Page 42: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/42.jpg)
𝜙=2𝜋 (𝑟2−𝑟1 )𝜆 =2𝜋 𝑑𝑠𝑖𝑛𝜃𝜆
• For two sources of waves, this equation finds the phase angle between them, depending on the location of the point where you measure the interference of the two waves.
![Page 43: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/43.jpg)
2 𝑡=𝑚𝜆𝑛• Thin film destructive reflection
![Page 44: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/44.jpg)
2 𝑡=(𝑚+ 12 )𝜆𝑛
• Thin film constructive reflection• Recall that is the wavelength in that medium
of index of refraction
![Page 45: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/45.jpg)
𝑎𝑠𝑖𝑛 𝜃=𝑚 𝜆• Single-slit diffraction• a is the width of the slit.• This equation gives diffraction minima• To get maxima, replace m with (m+1/2)
![Page 46: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/46.jpg)
𝛽=2𝜋 𝑎𝑠𝑖𝑛 𝜃𝜆• This equation gives for diffraction, which can
then be used to get the intensity of light at various points.
![Page 47: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/47.jpg)
• Intensity difference caused by single-slit diffraction.
• is calculated from a different equation
![Page 48: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/48.jpg)
• This equation combines the effects of two-slit interference and the diffraction caused by each of the slits independently.
![Page 49: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/49.jpg)
𝑅=𝜆Δ 𝜆=𝑁𝑚
• Used to find the chromatic resolving power for a diffraction grating
![Page 50: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/50.jpg)
𝑠𝑖𝑛𝜃1=1.22𝜆𝐷
• This is used to find the resolving power of a small circular hole of diameter D.
• is the location of the first minimum.
![Page 51: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/51.jpg)
2𝑑𝑠𝑖𝑛𝜃=𝑚𝜆• Used to find the location of maxima for
diffraction gratings
![Page 52: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/52.jpg)
![Page 53: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/53.jpg)
Answer: D
![Page 54: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/54.jpg)
![Page 55: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/55.jpg)
B, A
![Page 56: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/56.jpg)
![Page 57: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/57.jpg)
C, A
![Page 58: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/58.jpg)
![Page 59: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/59.jpg)
A,B
![Page 60: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/60.jpg)
![Page 61: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/61.jpg)
![Page 62: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/62.jpg)
• B
![Page 63: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/63.jpg)
![Page 64: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/64.jpg)
A,C
![Page 65: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/65.jpg)
![Page 66: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/66.jpg)
B
![Page 67: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/67.jpg)
![Page 68: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/68.jpg)
• C,B
![Page 69: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/69.jpg)
![Page 70: PHYS 222 SI Exam Review](https://reader035.vdocuments.us/reader035/viewer/2022062310/568164e6550346895dd74df9/html5/thumbnails/70.jpg)
A