EEE340Lecture : Inductances and Inductors L is the inductance of the circuit. It depends on the shape of the circuit. A circuit that has inductance is called an inductor.

EEE340Lecture 252 Mutual Inductances where The total energy due to L 1, L 2, and M 12 (or M 21 )

EEE340Lecture 253 Two close-by neighboring closed loops C 1 and C 2, flux The mutual inductance Where the flux linkage The self inductance (6.127) (6.125) (6.130) (6.129)

EEE340Lecture 254 Example: Find L 12 between a straight line and a triangle loop. Solution: (P.6-38) d I x y

EEE340Lecture 255 Example 6.16: Internal inductance. An air-filled coaxial cable has an inner conductor of radius a and a zero thickness outer of radius b. Find the per unit length inductance. Solution Energy method. The B-field can be obtained from Ampere’s law as I b a

EEE340Lecture 256 The magnetic energy has two parts: Within the conductor

EEE340Lecture 257 In the gap space

EEE340Lecture 258 Finally, the total inductance where the first term on the RHS is called the internal inductance and the second term is the external inductance. As frequency increases, skin-effect makes majority current on the conductor surface. As a result, the first term gradually vanishes. (6-140)