DOC PREVIEW
MIT 8 02T - Energy in Inductors

This preview shows page 1-2-17-18-19-36-37 out of 37 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 37 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 37 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 37 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 37 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 37 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 37 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 37 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 37 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

1P24-Class 24: OutlineHour 1:Inductance & LR CircuitsHour 2:Energy in Inductors2P24-Last Time:Faraday’s LawMutual Inductance3P24-Faraday’s Law of InductionBdNdtεΦ=−Changing magnetic flux induces an EMFLenz: Induction opposes change4P24-Mutual Inductance112 122 112122NMINMIΦ≡Φ→=212dIdtMε≡ −12 21MMM==A current I2in coil 2, induces some magnetic flux Φ12in coil 1. We define the flux in terms of a “mutual inductance” M12:You need AC currents!5P24-Demonstration:Remote Speaker6P24-This Time:Self Inductance7P24-Self InductanceWhat if we forget about coil 2 and ask about putting current into coil 1?There is “self flux”:111 111 NMILINLIΦ≡≡Φ→=dILdtε≡ −8P24-Calculating Self InductanceNLIΦ=Vs1 H = 1 A⋅Unit: Henry1. Assume a current I is flowing in your device2. Calculate the B field due to that I3. Calculate the flux due to that B field4. Calculate the self inductance (divide out I)9P24-Group Problem: SolenoidCalculate the self-inductance L of a solenoid (n turns per meter, length A, radius R)REMEMBER1. Assume a current I is flowing in your device2. Calculate the B field due to that I3. Calculate the flux due to that B field4. Calculate the self inductance (divide out I)LN I=Φ10P24-Inductor BehaviorIdILdtε= −LInductor with constant current does nothing11P24-dILdtε= −Back EMFI0, 0LdIdtε><I0, 0LdIdtε<>12P24-Inductors in CircuitsInductor: Circuit element which exhibits self-inductance Symbol:When traveling in direction of current:dILdtε= −Inductors hate change, like steady stateThey are the opposite of capacitors!13P24-PRS Question:Closing a Switch14P24-LR Circuit0iidIVLdtIRε==−−∑15P24-LR Circuit0 dI L dILIdt R dt RIRεε⎛⎞=⇒ =−−⎜⎟⎝⎠−−Solution to this equation when switch is closed at t = 0:()/() 1tIt eRτε−=−:LRtimeconstantLRτ=16P24-LR Circuitt=0+: Current is trying to change. Inductor works as hard as it needs to to stop itt=∞: Current is steady. Inductor does nothing.17P24-LR CircuitReadings on VoltmeterInductor (a to b)Resistor (c to a)ct=0+: Current is trying to change. Inductor works as hard as it needs to to stop itt=∞: Current is steady. Inductor does nothing.18P24-General Comment: LR/RCAll Quantities Either:()/FinalValue( ) Value 1tteτ−=−/0Value( ) Valuetteτ−=τ can be obtained from differential equation (prefactor on d/dt) e.g. τ = L/R or τ = RC19P24-Group Problem: LR Circuit1. What direction does the current flow just after turning off the battery (at t=0+)? At t=∞?2. Write a differential equation for the circuit3. Solve and plot I vs. t and voltmeters vs. t20P24-PRS Questions:LR Circuit & Problem…21P24-Non-Conservative FieldsR=100ΩR=10ΩBdddtΦ⋅=−∫EsGGI=1AE is no longer a conservative field –Potential now meaningless22P24-This concept (& next 3 slides) are complicated.Bare with me and try not to get confused23P24-Kirchhoff’s Modified 2nd RuleBiidVdNdtΦ∆=− ⋅ =+∑∫EsGGv0BiidVNdtΦ⇒∆− =∑If all inductance is ‘localized’ in inductors then our problems go away – we just have:0iidIVLdt∆−=∑24P24-Ideal Inductor• BUT, EMF generated in an inductor is not a voltage drop across the inductor!dILdtε=−inductor0Vd∆≡−⋅=∫EsGGBecause resistance is 0, E must be 0!25P24-Conclusion:Be mindful of physicsDon’t think too hard doing it26P24-Demos:Breaking circuits with inductors27P24-Internal Combustion EngineSee figure 1:http://auto.howstuffworks.com/engine3.htm28P24-Ignition SystemThe Distributor:http://auto.howstuffworks.com/ignition-system4.htm(A) High Voltage Lead(B) Cap/Rotor Contact(C) Distributor Cap(D) To Spark Plug(A) Coil connection(B) Breaker Points(D) Cam Follower(E) Distributor Cam29P24-Modern IgnitionSee figure:http://auto.howstuffworks.com/ignition-system.htm30P24-Energy in Inductor31P24-Energy Stored in InductordIIR Ldtε=+ +2dIIIR LIdtε=+()2212dIIR LIdtε=+BatterySuppliesResistorDissipatesInductorStores32P24-Energy Stored in Inductor212LULI=But where is energy stored?33P24-Example: Solenoid Ideal solenoid, length l, radius R, n turns/length, current I:0BnIµ=22oLnRlµπ=()22221122BoULI nRlIµπ==222BoBURlπµ⎛⎞=⎜⎟⎝⎠EnergyDensityVolume34P24-Energy Density Energy is stored in the magnetic field!22BoBuµ=: Magnetic Energy Density 22oEEuε=: Electric Energy Density35P24-Group Problem: Coaxial CableXIIInner wire: r=aOuter wire: r=b1. How much energy is stored per unit length? 2. What is inductance per unit length?HINTS: This does require an integralThe EASIEST way to do (2) is to use (1)36P24-Back to Back EMF37P24-PRS Question:Stopping a


View Full Document

MIT 8 02T - Energy in Inductors

Documents in this Course
Load more
Download Energy in Inductors
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Energy in Inductors and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Energy in Inductors 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?