Inductanceyên li dîwarê biçûkê

Sababê Induktansiyê Transmission Line

Girîngî, elektrikî nîrgirî di transmission line de bi AC hêsan voltage û current da tarîde. Hêsan alternating current ji bo şûrên didan di conductor de taybetmendîya magnetic fluxê ya hêsan bi alternating nature pêşkêş dide. Ev hêsan alternating magnetic flux bikarhêner li ser conductors din ên paralel bia main conductor linkage bike. Flux linkage di conductor de navbera jî û derve digire. Navbera flux linkage di navbera xwe û derve flux linkage di derve flux de ye. Niha termi induktansi ya qetê bi flux linkage re tê gotin, bi λ piştgirî kirin. Li gûtî yek coil bi N number of turn linked by flux Φ ji bo current I, ewa,

Lê di transmission line de N = 1. Divê mîna value of flux Φ hesab bikin, û lêra, divê transmission line inductance bigihin.

Hesabkirina Induktansiyê Conductor Yekane

Hesabkirina Induktansiyê Navbera bi Magnetic Flux Navbera Conductor

Li gûtî yek conductor bi current I da şûrên didan di length l de, x radius navbera conductor û r radius original conductor e. Niha cross-sectional area bi rêjeya radius x piştgirî kirin πx2 square – unit û current Ix di vê cross-sectional area de tarîde. Naha value of Ix bi rêjiyê original conductor current I û cross-sectional area πr2 square – unit pêşkêş dide

Niha thickness dx bi 1m length of the conductor, li gûtî Hx magnetizing force ji bo current Ix around the area πx2.

Û magnetic flux density Bx = μHx, li gûtî μ permeability of this conductor e. Tenê, µ = µ0µr. Li gûtî relative permeability of this conductor µr = 1, tenê µ = µ0. Lela, here Bx = μ0 Hx.

dφ for small strip dx expressed by

Here entire cross-sectional area of the conductor does not enclose the above expressed flux. The ratio of the cross sectional area inside the circle of radius x to the total cross section of the conductor can be thought about as fractional turn that links the flux. Therefore the flux linkage is

Now, the total flux linkage for the conductor of 1m length with radius r is given by

Hence, the internal inductance is

External Inductance due to External Magnetic Flux of a Conductor

Let us assume, due to skin effect conductor current I is concentrated near the surface of the conductor. Consider, the distance y is taken from the center of the conductor making the external radius of the conductor.

Hy is the magnetizing force and By is the magnetic field density at y distance per unit length of the conductor.

Let us assume magnetic flux dφ is present within the thickness dy from D1 to D2 for 1 m length of the conductor as per the figure.

As the total current I is assumed to flow in the surface of the conductor, so the flux linkage dλ is equal to dφ.

But we have to consider the flux linkage from conductor surface to any external distance, i.e. r to D

Inductance of Two Wire Single Phase Transmission Line

Suppose conductor A of radius rA carries a current of IA in opposite direction of current IB through the conductor B of radius rB. Conductor A is at a distance D from conductor B and both are of length l. They are in close vicinity with each other so that flux linkage takes place in both of the conductors due to their electromagnetic effects.

Let us consider the magnitude of current in both conductors are same and hence I