Self - Inductance • Faraday postulated that a magnetic field consists of lines of force surrounding the current-carrying conductor. • Think of these lines as elastic bands that close on themselves. • As the current increases and decreases, the bands expand and collapse about the conductor. ECE 201 Circuit Theory I 1 Self – Inductance continued Compress for decreasing magnetic field (due to decreasing current). Faraday’s Law : the voltage induced into the conductor is proportional to the number of lines that cut the conductor. Expand for increasing magnetic field (due to increasing current). ECE 201 Circuit Theory I 2 Faraday’s Law d v dt λ is called the “flux linkage” and is measured in weber-turns ECE 201 Circuit Theory I 3 Magnetic field linking an N-turn coil N PNi ECE 201 Circuit Theory I 4 Permeance, P • Permeance describes the magnetic properties of the space occupied by the flux. • Linear for non-magnetic materials • Units are webers/ampere-turn. ECE 201 Circuit Theory I 5 d d ( N ) v dt dt d d vN N (PNi ) dt dt di di 2 vN P L dt dt LN 2 Self - Inductance ECE 201 Circuit Theory I 6 Voltage Polarity • When i increases, di/dt is + and v is +. – Energy produces the magnetic field ECE 201 Circuit Theory I 7 Voltage Polarity • When i decreases, di/dt is - and v is -. – i is still + – Magnetic field collapses - + ECE 201 Circuit Theory I 8