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Physics 212 HKN Exam 3 Review Session
Steven Kolaczkowski Kanad sarkar
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RC Circuits Capacitors instantaneous reaction and time dependence.
At π‘=0 At π‘ ββ π=πΌπ
only works for resistors. Donβt try and apply this to capacitors and sources!!! Time constant (π): The fundamental time of a circuit π π
πΆ =π
πΆ = π ππ We will have another time constant for LR and LC circuits Power Ξ£ π π π =0 Conservation of Energy, time independent π=πΌπ = πππ‘π‘π
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LR Circuits KVL and KCL still apply! (And always will)
π πΏ =πΏ ππΌ ππ‘ π π
=πΌπ
Inductors will never drastically change current Same as a Capacitors relation to Voltage π‘=0 π‘ββ New Time Constant!!! π πΏπ
= πΏ π
π π
πΆ =π
πΆ
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LC Oscillators and LRC DC Circuits
For LC circuits, energy alternates between being stored in electric fields (in C) and magnetic fields (in L) π πΏ = 1 2 πΏ πΌ π πΆ = 1 2 πΆ π π πΏ + π πΆ =ππππ π‘πππ‘= π πππ₯ 2 2πΆ π π‘ =ππππ (ππ‘+π) where π πΏπΆ = 1 πΏπΆ and π is based on the initial conditions LRC Damped Oscillators: π 2 = π πΏπΆ 2 β π½ π½= π
2πΏ Critical Damping: π
=2 πΏ πΆ
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Phasors, Reactance, and Phase Relations
Phasor: A rotating 2D vector whose components can be mapped to physical quantities. In this class we will only deal with single frequencies and the vertical projection Want to find out what the horizontal projection is? Want to see what happens when you excite multiple frequencies? Take ECE 210! Reactance: The relation between Voltage and Current for non-resistive, linear devices In this class, you can think of reactance as the βresistanceβ of Capacitors and Inductors π πΆ = 1 ππΆ = Ξ© π πΏ =ππΏ = Ξ© Phase Relations Capacitive circuits have π πΆ π‘ lag πΌ πΆ (π‘) by 90Β° Inductive circuits have π πΏ (π‘) lead πΌ πΏ (π‘) by 90Β°
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Impedance and AC Circuits
Impedance (Z): The effective βtotalβ resistance of the circuit π 2 = π
π πΏ β π πΆ π π = πΌ π π This looks just like Ohmβs Law!!! What are the units of π? All components will rotate at angular frequency π set by the generator There will be a phase difference between the generator voltage and the generator current π π= tan β1 π πΏ β π πΆ π
Power consumption: Both Capacitors and Inductors do not absorb power. < π πΊππππππ‘ππ > = < π π
ππ ππ π‘ππ > = πΌ π π π cos π
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Transformers A way of transforming an AC Signal to another AC Signal
π π = π π π π π π πΌ π = π π π π πΌ π πΌ π π π = πΌ π π π
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Adjustments to Maxwellβs Equations
Changes to Ampereβs Law and a little bit of history π΅ βπ π = π 0 πΌ πππ = π 0 πΌ+ πΌ π· = π 0 πΌ+ π 0 π Ξ¦ πΈ ππ‘ Maxwellβs Equations: Gaussβ Laws: πΈ βπ π΄ = π πππ π π΅ βπ π΄ =0 Faradayβs Law: πΈ βπ π =β π ππ‘ β« π΅ βπ π΄
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Wave Equations and Important Relations
General Wave Equation: π 2 β π π₯ 2 = 1 π£ 2 π 2 β π π‘ 2 General Wave Solution: β π₯,π‘ =π΄πππ (ππ₯βππ‘ +π) This is a wave traveling in the positive x direction Propagation in media π 0 βπ π 0 βπ π£= π π π= ππ π 0 π 0 Very important relations: π= 2π π = π β π=2ππ = ππππ π π£= π π =ππ = π π π 2 = π 0 π 0 π΅β₯πΈ π΅ 0 = πΈ 0 π = πΈ π 0 π 0
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A Hint of Relativity and Quantum
Doppler Shift: The change in frequency of a wave as it is approaching or departing from an observer. π½β‘ π£ π Blue Shift (wave travelling towards you): π β² =π 1+π½ 1βπ½ Red Shift (wave travelling away from you): π β² =π 1βπ½ 1+π½ Poynting Vector: A vector quantity that describes the transfer of energy in a wave π β‘ πΈ Γ π΅ π 0 = πππ‘π‘π π <π> = 1 2 π π 0 πΈ 2 = π 0 π πΈ 2 = π Photons (πΎ): Particles of light πΈ πΎ =βπ=βπ π πΎ = πΈ π = β π
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Polarization πΈ π§,π‘ = π₯ πΈ 1 cos ππ§βππ‘+ π 1 + π¦ πΈ 2 cosβ‘(ππ§βππ‘+ π 2 )
Linear Polarization: π 1 = π 2 Β±ππ for integer π Law of Malus: πΌ= πΌ 0 cos 2 (π) If incident light is Unpolarized πΌ= πΌ 0 Circular Polarization: π 1 = π 2 Β± π 2 AND πΈ 1 = πΈ 2 Cosine leads Sine RCP: πππππ Γππππ =ππππππππ‘πππ LCP: πππππ Γππππ =βππππππππ‘πππ Birefringence: Materials that cause a delay for one polarization of light, but not others Quarter-Wave Plate: Uses a slow axis and a fast axis to change certain linear polarizations to circular polarizations
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Optics Propagation in media π 0 βπ π 0 βπ π£= π π π= ππ π 0 π 0
Snellβs Law: π 2 π ππ π 2 = π 1 π ππ π 1 Total Internal Reflection: When there is no transmitted light π π = sin β1 π 2 π 1 Brewsterβs Angle: When angle between Reflected and Refracted ray is 90Β° Reflected light is polarized perpendicular to plane of incidence tan π 1 = π 2 π 1
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Lenses 1 π + 1 π β² = 1 π where π is the object distance, π β² is image distance, and π is focal length π is ALWAYS positive Magnification: the ratio of image height to object height. π= β β² β =β π β² π π=β π π βπ π β² = ππ π βπ Converging Lenses: π>0 Diverging Lenses: π<0 Virtual Image: π β² <0 Principle rays: Horizontal to focus and through center of lens
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Exam Advice Know when and how to use your equation sheet
Donβt panic, just keep on moving Make sure you are in the right mindset going into the exam Spend your time showing what you know DONβT CHEAT Check you units!!!
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Past Exam Questions
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Spring 2017
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Fall 2010
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Spring 2015
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Fall 2010
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Fall 2010
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Fall 2010
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Spring 2013
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Fall 2015
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