Prozorov_20 - PHYSICS 222 Introduction to Classical Physics...

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Unformatted text preview: PHYSICS 222 Introduction to Classical Physics II Prof. Ruslan Prozorov Iowa State University Fall 2011 LECTURE 20 Inductance. Energy of magnetic field. RL Circuit mutual inductance PHYS222 - Lecture 20 - Prof. Ruslan Prozorov - Iowa State University 10 October 2011 2 Induction between two coils Change the current in coil 1 changes the B-flux through coil 2 induces an emf in coil 2 PHYS222 - Lecture 20 - Prof. Ruslan Prozorov - Iowa State University 10 October 2011 3 PHYS222 - Lecture 20 - Prof. Ruslan Prozorov - Iowa State University 10 October 2011 4 Mutual inductance d 21 di1 2 N2 M 21 dt dt N 2 21 M 21 i1 M21 mutual inductance indicates how large is an emf in 2 due to current change in 1 Of course it works both ways: di2 1 M12 dt N1 12 M12 i2 PHYS222 - Lecture 20 - Prof. Ruslan Prozorov - Iowa State University 10 October 2011 5 Mutual inductance depends on the geometry, orientation and materials of the coils. It can be shown that M21 M12 M Therefore, we have: di2 1 M dt di1 2 M dt N2 21 N1 12 M i1 i2 Units: SI Henry 1 H = 1 Wb/A PHYS222 - Lecture 20 - Prof. Ruslan Prozorov - Iowa State University 10 October 2011 6 mutual inductance of two solenoids l B2 0 n2i2 12 0 n2i2 R12 flux in solenoid 1 due to field produced by solenoid 2 n112 n1 ( 0 n2i2 R12 ) M 0 n1n2 R12 i2 i2 PHYS222 - Lecture 20 - Prof. Ruslan Prozorov - Iowa State University mutual inductance per unit length 10 October 2011 7 self-inductance Ideal coil (no resistance) If current through coil changes, flux through coil changes in each loop there is an induced emf loops “in series” emf induced between two ends of coil Single coil is called an inductor The effect is called self-induction PHYS222 - Lecture 20 - Prof. Ruslan Prozorov - Iowa State University L di dt N B L i 10 October 2011 8 real inductors PHYS222 - Lecture 20 - Prof. Ruslan Prozorov - Iowa State University 10 October 2011 9 inductors work against di/dt Inductor always acts to oppose current change. setting up a current in a circuit with an inductor will take some time. used in circuit design to protect against rapid changes of currents or spikes PHYS222 - Lecture 20 - Prof. Ruslan Prozorov - Iowa State University 10 October 2011 10 resistors and inductors PHYS222 - Lecture 20 - Prof. Ruslan Prozorov - Iowa State University 10 October 2011 11 RL circuits: current growth Kirchhoff’s law iR L di 0 dt i t 0 0 Differential equation for i + initial condition i t 0 0 i t (no inductor) R PHYS222 - Lecture 20 - Prof. Ruslan Prozorov - Iowa State University Qualitatively: 10 October 2011 12 di iR L 0 dt i ln R R di R dt L i R R t L R R ln 1 i t L i R i t R R t 1 e L t 1 e L R If L is large, is large, i.e. current grows slowly. PHYS222 - Lecture 20 - Prof. Ruslan Prozorov - Iowa State University 10 October 2011 13 in-class example: RL circuit You have 1000 Ω resistor and you want to build an LR series circuit that will go from 0 to 0.9 V0/R in 1 ms once the switch is closed. What value should L have? R L i t R V0 t 1 e 0.9 1 e L R 1 ms 1 ms ln 0.1 0.43 ms L R 0.43 H PHYS222 - Lecture 20 - Prof. Ruslan Prozorov - Iowa State University 10 October 2011 14 inductor networks parallel connection PHYS222 - Lecture 20 - Prof. Ruslan Prozorov - Iowa State University series connection 10 October 2011 15 inductors store energy After the switch is opened, the inductor drives the current through the resistor. The energy dissipated in the resistor must have been stored in the inductor. PHYS222 - Lecture 20 - Prof. Ruslan Prozorov - Iowa State University 10 October 2011 16 energy stored in an inductor To establish current (from i = 0 to i = I ): di V L dt Voltage across inductor: (ignoring signs) 1) rate of energy supplied to inductor P Vi Li di dt 2) increase of energy within inductor dU Pdt Li di I 3) energy stored within inductor U dU L idi 0 1 U LI 2 2 PHYS222 - Lecture 20 - Prof. Ruslan Prozorov - Iowa State University 10 October 2011 17 ignition coil An ignition coil (also called a spark coil) is an induction coil in an automobile's ignition system which transforms the battery's 12 volts (6 volts in some older vehicles) to the thousands of volts (20 to 30 thousand volts or more) needed to spark the spark plugs. This specific form of the autotransformer, together with the contact breaker and a capacitor converts low voltage from a battery into the high voltage required by spark plugs in an internal combustion engine. PHYS222 - Lecture 20 - Prof. Ruslan Prozorov - Iowa State University 10 October 2011 18 ...
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