Lecture 10 Induction Applications Chapter 20.6  20.8 Outline Self-Inductance RL Circuits Energy Stored in a Magnetic Field

Self-Inductance Faraday’s law prevents the current in a circuit to reach the maximum value immediately. The magnetic flux through the loop increases together with the current. As a result, an induced emf appears and opposes the change in magnetic flux. The opposing emf results in a gradual increase of the current. The effect is called self-inductance. I R B

Magnitude of Self-Inductance The self-induced emf is proportional to the time rate of change of the current.  I ℇ =  L   t L is called inductance ℇ =  N  B /  t The SI unit of inductance is henry 1 H = 1 V s / A N  B /  t = L  I /  t  L = N  B /  I = N  B /I

RL Circuits Solenoids or closely wrapped coils have a large inductance and are called inductors.inductors For a circuits with a resistor ℇ  IR = 0 and  V=  IR. Resistance is a measure of opposition to the current. Inductance is a measure of opposition to the rate of change in current ( ℇ =  L  I /  t). For a circuit with both a resistor and an inductor, the current is unable to reach its maximum value instantaneously. We can define a time constant for such a circuit as  = L/R.circuit

Problem with an RL Circuit Problem: A circuit has a 10-V battery, a 5-  resistor, and a 20-mH inductor. Find the circuit time constant and the current after 1 time constant.  = L/R =  2 H / 5  = 0.04 s I = ℇ/ R (1  e  Rt/L ) t =   1  e  1 = I = ℇ /R = V / 5  = 1.26 A

Energy Stored in a Magnetic Field The battery has to do work to produce a current. This work is energy stored by the inductor in its magnetic field. The energy stored by an inductor is similar to that of a capacitor. L I 2 PE L =  2 C  V 2 PE C =  2

Summary Self-inductance is a phenomenon of opposing to a change in current in electric circuits due to appearance of the magnetic field. Inductor is an element with a large inductance. Energy stored by an inductor is similar to that stored by a capacitor.