INDUCTANCE AND INDUCTORS

Inventions 1  Alexander Fleming, discovered 'penicillin'  In 1922, Fleming was working on a drug to kill the harmful bacteria.  While working, Fleming's nose leaked, dropping some mucus onto the dish.  The bacteria started to disappear.  He had discovered a natural substance found in tears and nasal mucus that helps the body fight germs but not adversely affecting the human body.

Inventions 2  The Microwave Oven  Percy Spencer, an American engineer was working on active radar set when he noticed that chocolate in his pocket started to melt.  Microwaves from the radar had melted the food in his pocket.

Experimentation  Faraday wound two coils on an iron ring and energized one of them from a battery  As he closed the switch energizing the first coil, Faraday noticed that a momentary voltage was induced in the second coil,  And when he opened the switch, he found that a momentary voltage was again induced but with opposite polarity.  When the current was steady, no voltage was produced at all.

Electromagnetic Induction

 In (a), a magnet is moved through a coil of wire, and this action induces a voltage in the coil.  When the magnet is thrust into the coil, the meter deflects upscale; when it is withdrawn, the meter deflects downscale, indicating that polarity has changed.  The voltage magnitude is proportional to how fast the magnet is moved.  In (b), when the conductor is moved through the field, voltage is induced.

Electromagnetic Induction

 In (c), voltage is induced in coil 2 due to the magnetic field created by the current in coil 1.  In (d) voltage is induced in a coil by its own current. At the instant the switch is closed, the top end of the coil becomes positive, while at the instant it is opened, the polarity reverses and the top end becomes negative.

Electromagnetic Laws Faraday’s Law  Based on these observations, Faraday concluded that voltage is induced in a circuit whenever the flux passing through the circuit is changing and that the magnitude of the voltage is proportional to the rate of change of the flux. Lenz’s Law  Heinrich Lenz (a Russian physicist, 1804–1865) determined a companion result. He showed that the polarity of the induced voltage is such as to oppose the cause producing it.

Induced Voltage and Induction  Note: This voltage does not oppose current, it opposes only changes in current.

Induced Voltage  Flux is directly proportional to current  Induced voltage is proportional to the rate of change of flux, and since flux is proportional to current, induced voltage will be proportional to the rate of change of current  Let the constant of proportionality be L.

Example  Inductance, L= 5 m H and current through it changes at the rate of 1000 A/s, What is induced voltage?

Inductance  where l is in meters, A is in square meters, N is the number of turns, and mue is the permeability of the core.

Computing Induced Voltage  L=10 m H, Determine v L

Computing Induced Voltage

Example  Find Equation for voltage across inductor  L=12.5 H, i=te -t Amps

Inductance in Series/Parallel

Inductance and steady state DC  The voltage across an ideal inductance with constant dc current is zero because the rate of change of current is zero. (a).  Since the inductor has current through it but no voltage across it, it looks like a short circuit,(b).  In general, an ideal inductor looks like a short circuit in steady state dc.  (This should not be surprising since it is just a piece of wire to dc.)

Inductance and steady state DC

Example  In Fig. a, the coil resistance is 14.4 ohm. What is the steady state current I ?

Example  The resistance of coil 1 in Fig. (a), is 30 ohm and that of coil 2 is 15 ohm. Find the voltage across the capacitor assuming steady state dc.