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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
• These equations are what let you find the major constants that do not change with time.
• Remember, capital letters are not time dependent.
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
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.
𝐼 𝑟𝑎𝑣=2𝜋𝐼
• Not mentioned in class really
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.
How to determine v(t), i(t),
• The current phasor is parallel with the phasor.• leads , and lags • The voltage – I.E. if then
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.
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.
Example #2
• Let’s say that in an LRC circuit,
• Also suppose that you’ve calculated the phase angle to be, and
• Then
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.
𝑝=𝑖𝑣• Equation relating power, current, and voltage
𝑃𝑎𝑣𝑒𝑟𝑎𝑔𝑒=12𝐼𝑉𝑐𝑜𝑠𝜙=𝐼 𝑟𝑚𝑠𝑉 𝑟𝑚𝑠𝑐𝑜𝑠𝜙=𝐼 𝑟𝑚𝑠
2 𝑅
• Average power in an LRC AC circuit
𝑉 2
𝑉 1
=𝑁 2
𝑁 1
• Equations used to convert a voltage inside a transformer
𝑉 1 𝐼 1=𝑉 2 𝐼2• Current and voltage in a transformer
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
𝑐=1
√𝜖0𝜇0• Speed of light related to two constants
𝑢=12𝜖0𝐸
2+ 12𝜇0
𝐵2=𝜖0𝐸2=𝐵2
𝜇0
• Energy density
𝑃=𝐹𝐴
=1𝐴𝑑𝑝𝑑𝑡
=𝑆𝑐
=𝐸𝐵𝜇0𝑐
• Equations relating the radiation pressure of an electromagnetic wave to the poynting vector and E and B.
𝑺=1𝜇0
𝑬×𝑩
• Poynting vector.• Note that the poynting vector is perpendicular
to both E and B
𝐼=𝑆𝑎𝑣𝑒𝑟𝑎𝑔𝑒=𝐸𝑚𝑎𝑥𝐵𝑚𝑎𝑥
2𝜇0=𝐸𝑚𝑎𝑥2
2𝑐𝜇0=12 √ 𝜖0𝜇0 𝐸𝑚𝑎𝑥
2 =12𝜖0𝑐 𝐸𝑚𝑎𝑥
2
• The intensity of electromagnetic radiation, related to the E field.
• Equations relating the speed of light c, the wavelength of light , the frequency of light the angular frequency , and the wave number .
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 (
𝜃𝑖=𝜃 𝑟𝑅𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛• The equations for reflection and refraction
𝐼=𝐼𝑚𝑎𝑥cos (𝜙 )2
• The equation for intensity of light through a diffraction grating.
•
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.
𝑡𝑎𝑛𝜃𝑃=𝑛2𝑛1
• Equation used to find Brewster’s Angle, also known as the Polarization Angle .
• This angle is where reflection stops happening.
1𝑠+1
𝑠′=1𝑓
• The master equation for both lenses AND mirrors
• 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
𝑚= 𝑦 ′
𝑦=− 𝑠
′
𝑠• Magnification caused by a mirror or lens
𝑓 h𝑠𝑝 𝑒𝑟𝑖𝑐𝑎𝑙𝑚𝑖𝑟𝑟𝑜𝑟=𝑅2
• Focal point of a spherical mirror
1𝑓=(𝑛−1 )( 1𝑅1−
1𝑅2
)• “Lensmaker’s Equation”
𝑛𝑎𝑠
+𝑛𝑏𝑠′
=𝑛𝑏−𝑛𝑎𝑅
• Look up
𝑚= 𝑦 ′
𝑦=−
𝑛𝑎𝑠′
𝑛𝑏 𝑠
• Spherical fish bowls is the main application of this equation
𝑀= 𝜃′
𝜃
• M is the angular magnification of a telescope.• Recall that and
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)
𝑑𝑠𝑖𝑛𝜃=(𝑚+ 12 )𝜆
• Destructive interference.
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.
𝐼=𝐼𝑚𝑎𝑥cos ( 𝜃2 )2
• In single slit diffraction, you can use this equation to find the intensity as a function of the angle.
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.
2 𝑡=𝑚𝜆𝑛• Thin film destructive reflection
2 𝑡=(𝑚+ 12 )𝜆𝑛
• Thin film constructive reflection• Recall that is the wavelength in that medium
of index of refraction
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)
𝛽=2𝜋𝑎𝑠𝑖𝑛 𝜃𝜆
• This equation gives for diffraction, which can then be used to get the intensity of light at various points.
• Intensity difference caused by single-slit diffraction.
• is calculated from a different equation
• This equation combines the effects of two-slit interference and the diffraction caused by each of the slits independently.
𝑅=𝜆Δ 𝜆
=𝑁𝑚
• Used to find the chromatic resolving power for a diffraction grating
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.
2𝑑𝑠𝑖𝑛𝜃=𝑚𝜆• Used to find the location of maxima for
diffraction gratings
Answer: D
B, A
C, A
A,B
• B
A,C
B
• C,B
A