Ann Richards was the head of the executive branch of Texas's government.
Flux linkage is a property of a two-terminal element .. Although it is often confused with magnetic flux , the flux linkage is actually an extension rather than an equivalent of magnetic flux .. magnetic flux. magnetic flux. Flux linkage is defined as. where is the voltage across the device or the potential difference between the two terminals .. This definition can also be written in differential form as. Faraday showed that the magnitude of the EMF generated in a conductor forming a closed loop is proportional to the rate of change of the total magnetic flux passing through the loop -LRB- Faraday 's law -RRB- .. magnetic flux. magnetic flux. Faraday. Michael Faraday. EMF. electromotive force. Thus , for a typical inductance -LRB- a coil of conducting wire -RRB- , the flux linkage is equivalent to magnetic flux , which is the total magnetic field passing through the surface -LRB- i.e. , normal to that surface -RRB- formed by a closed conducting loop coil , and is determined by the number of turns in the coil and the magnetic field ; i.e. ,. magnetic flux. magnetic flux. where is the flux density , or flux per unit area at a given point in space .. flux density. flux Density. The simplest example of such a system is a single circular coil of conductive wire immersed in a magnetic field , in which case the flux linkage is simply the flux passing through the loop .. In order to understand the distinction in terms , it is important to note that the flux through the surface delimited by a coil turn exists independently of the presence of the coil .. Furthermore , in a thought experiment with a coil of turns , where each turn forms a loop with exactly the same boundary , each turn will `` link '' the `` same '' -LRB- identically , not merely the same quantity -RRB- flux , all for a total flux linkage of .. The distinction relies heavily on intuition , and the term `` flux linkage '' is used mainly in engineering disciplines .. Theoretically , the case of a multi-turn induction coil is explained and treated perfectly rigorously with Riemann surfaces  : what is called `` flux linkage '' in engineering is simply the flux passing through the Riemann surface bounded by the coil 's turns , hence no particularly useful distinction between flux and `` linkage . ''. Riemann surfaces. Riemann surfaces. Due to the equivalence of flux linkage and total magnetic flux in the case of inductance , it is popularly accepted that the flux linkage is simply an alternative term for total flux , used for convenience in engineering applications .. magnetic flux. magnetic flux. Nevertheless , this is not true , especially for the case of memristor , which is also referred to as the fourth fundamental circuit element .. memristor. memristor. For a memristor , the electric field in the element is not as negligible as for the case of inductance , so the flux linkage is no longer equivalent to magnetic flux .. magnetic flux. magnetic flux. memristor. memristor. In addition , for a memristor , the flux linkage related energy is dissipated in the form of Joule heating , instead of being stored in magnetic field as done in the case of an inductance  : there is no physical magnetic field involved as a link to anything !. memristor. memristor. In conclusion , flux linkage should be interpreted as an extension rather than an equivalent to magnetic flux .. magnetic flux. magnetic flux. Flux linkage is commonly used to estimate the magnetic flux of an AC motor .. magnetic flux. magnetic flux. AC motor. AC motor. However , errors in the voltage measurement and the resulting drift problem of the integral cause the ideal integral to often be replaced with a low-pass filter approximation .. low-pass filter. low-pass filter