john
Uploaded by
19 SLIDES
757 VUES
210LIKES

Inductance

DESCRIPTION

Inductance. General Physics II, Spring 2011 Brian Meadows University of Cincinnati. Outline. What is Inductance and what are the units? Self Inductance of solenoid Series Inductance and Resistance (L-R) circuits Energy in magnetic field Mutual Inductance. Outline.

1 / 19

Télécharger la présentation

Inductance

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Inductance General Physics II, Spring 2011 Brian Meadows University of Cincinnati Brian Meadows, U. Cincinnati.

  2. Outline • What is Inductance and what are the units? • Self Inductance of solenoid • Series Inductance and Resistance (L-R) circuits • Energy in magnetic field • Mutual Inductance Brian Meadows, U. Cincinnati

  3. Outline • What is Inductance and what are the units? • Self Inductance of solenoid • Series Inductance and Resistance (L-R) circuits • Energy in magnetic field • Mutual Inductance Brian Meadows, U. Cincinnati

  4. Inductance • When a current flows in a circuit, it produces a magnetic field linkage • E.g. a current in a solenoid of N turns produces a magnetic field B that creates a flux NB in itself. • A flux linkage with another circuit can also be established • The former is “self inductance”, the latter is “mutual inductance” (n = N/L) i B = 0ni NB = nLBA = 0n2LAi L Brian Meadows, U. Cincinnati

  5. Inductance and Self Inductance • The flux linkage NBis proportional to the current i that produces it. NB = L i (analogous to C in q= CV ) • The unit of inductance is the henry (H) [L] = [B]/[A] so 1 H = 1 T.m2/A • The self-inductance of a solenoid of length Land area A with n turns per unit length an is given by L = 0 n2 LA Brian Meadows, U. Cincinnati

  6. Inductance • When a current in a circuit changes, it produces a changing magnetic field dB/dt = 0 • If the magnetic field changes, then a “back EMF” e is induced in a direction that will always oppose the change in current that is causing the field to change. • If i comes in as illustrated, and di/dt>0, then e is in direction indicated. i - + e = L di/dt Brian Meadows, U. Cincinnati

  7. Outline • What is Inductance and what are the units? • Self Inductance of solenoid • Series Inductance and Resistance (L-R) circuits • Energy in magnetic field • Mutual Inductance Brian Meadows, U. Cincinnati

  8. Series R-C Circuit (reminder) • Apply Kirchoff rule 2 to series circuit: VC= Q/C • Start at bottom right and go clockwise: • Solve this equation: • Charge rises slowly to peak value - + -q(t) +q(t) i=dq/dt + C R i=dq/dt VR= iR -  Brian Meadows, U. Cincinnati

  9. Series L-R Circuit • Apply Kirchoff rule 2 to series circuit: VL= L di/dt • Start at bottom right and go clockwise: • Solve this equation: • Current rises slowly to peak value - + i + i L R VR= iR  - Open switch (no effect) Brian Meadows, U. Cincinnati

  10. Current build-up in LR circuit This is reduced by factor “e” each time interval L/R i(t) i(1)=e/R i(0)=0 t Circuit “time constant” is L/R. This is zero if L=0. Brian Meadows, U. Cincinnati

  11. Now remove the EMF and allow current to drop: VL= L di/dt • Start at bottom right and go clockwise: • Solve this equation: • Current drops slowly from initial value to - + i + i L R VR= iR - Close switch (shorts EMF so   0) Brian Meadows, U. Cincinnati

  12. Current decay in LR circuit i(t) i(0)=e/R This is reduced by factor “e” each time interval L/R i(1)=0 t Circuit “time constant” is L/R. This is zero if L=0. Brian Meadows, U. Cincinnati

  13. Outline • What is Inductance and what are the units? • Self Inductance of solenoid • Series Inductance and Resistance (L-R) circuits • Energy in magnetic field • Mutual Inductance Brian Meadows, U. Cincinnati

  14. Energy in Magnetic Field • Energy is required to build up current (and B field) in L: VL= L di/dt • Power P = i VLso energy is • This leads to: • Recall, for a capacitor, electric field energy is - + i + i L R VR= iR  - Open switch (no effect) Brian Meadows, U. Cincinnati

  15. Outline • What is Inductance and what are the units? • Self Inductance of solenoid • Series Inductance and Resistance (L-R) circuits • Energy in magnetic field • Mutual Inductance Brian Meadows, U. Cincinnati

  16. Mutual Inductance – Pair of Coils • Flux linkage due to coil 1 in coil 2, N21 2/ i1 so • Likewise • Therefore Brian Meadows, U. Cincinnati

  17. Example – Solenoid and Short Coil • Flux linkage due to solenoid (s) in coil (c) is Nc s c = M is • This flux linkage is • Therefore Turns/m = n Field B = 0 n is Area A=r12 Nc total turns Brian Meadows, U. Cincinnati

  18. Example • Solenoid has n=2000 turns/m and r=5 cm, coil has Nc=50 turns. What is e in coil if dis/dt = 0.1 A/s ? • So • Therefore, EMF induced in coil is Turns/m = n Field B = 0 n is Area A=r12 Nc total turns Brian Meadows, U. Cincinnati

  19. Example - Transformer • Has “primary (NP turns) and “secondary” (NS turns) coils. • Iron form ensures that virtually ALL flux through primary also passes through secondary. • fP/NPandfS/NS • dfP /dtNPanddfS /dt/NS • So eS/eP= NS / NP Brian Meadows, U. Cincinnati

More Related