PHYS208 PHYS208 4/20 Class

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Inductance and LR Circuits

Quote of the Day

Wrap up Lenz's Law

DEMONSTRATION: "Magic Tube"

Concept Check

Comparison of Two Important Situations

Parallel Conducting Plates   Solenoid
 
Charged capacitor
 
   
Energized inductor
 
Definition of Capacitance   Analogous Definition?
 
Definition of capacitance
 
  For discussion today...
Electrical Energy Stored   Magnetic Energy Stored?
 
Energy stored in capacitor
 
  For discussion next class...

Mutual Inductance

We have already seen that changing magnetic flux will induce current in a closed loop. If the current in coil #1 below is changed, the magnetic field that it creates will change. Thus the magnetic flux in coil 2 will change and a current will be induced in that loop as a result. These coils are said to be linked magnetically and are said to have a mutual inductance.

Two linked coils

What if the two coils above were part of a single coil? A change in current in that coil will also induce an emf in that same coil by Faraday's law. This is known an self-induction and we will focus our attention on self-inductance today (rather than mutual inductance).

Flux Linkage

The concept of flux linkage is useful when considering multiple identical turns; that is, N identical turns linked by the same magnetic flux. For N identical turns, Faraday's law becomes

Faraday's law for multiple identical turns

where the quantity in parentheses is the so-called flux linkage.

Self-inductance

Charge Separation on Two Conductors   Flux Linked by Identical Turns
 
Charge separation is proportional to potential difference

Regardless of size, shape and geometric arrangement of two conductors, the charge separation (charge moved from one conductor to another while maintaining no net charge) is always observed to be proportional to the potential difference between the two conductors. The capacitance is defined to be the proportionality constant.
 
   
Magnetic flux is proportional to current

Regardless of size and shape of conducting turns, the flux linkage coupling the turns is always observed to be proportional to the current in the loops. The self-inductance is defined to be the proportionality constant.
Definition of Capacitance   Definition of Inductance
 
Capacitance is the proportionality constant
 
   
Self-Inductance is the proportionality constant
 

Any portion of a circuit involving flux linkage may be assigned an inductance; such a device is known as an inductor. In subsequent classes we will investigate means of evaluating inductance, which involves the geometric factors of the "coil" configuration. Today we will focus our remaining attention on some of the circuit behavior of inductors.

For the time being, recognize that Faraday's law for an inductor (with constant inductance) may be rewritten as:

Faraday's law for the inductor

A self emf is induced in an inductor whenever the current changes. The negative sign is still Lenz's law; that is, the direction of the self-induced emf will oppose the change in current.

LR Circuits

Not yet available...


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Last updated April 21, 1998.
Copyright George Watson, Univ. of Delaware, 1997.