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EEE340Lecture 251 6-11: 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.

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

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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)

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

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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

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

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EEE340Lecture 257 In the gap space

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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)

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