uniform current density formula

Current density refers to the amount of charge flowing through a specific cross-sectional area of a conductor. In this equation, ‘I’ is the amount of current in Amperes while ‘A’ is the cross-section area in sq. Conductors with a uniform cross-section and uniform flow of electric current can use the formula ρ =R A/l. The SI unit of current density is Ampere/metre2. of copper wire conducts a current flow of 2mA. 1) I do not have a clear idea of what js represents. Together, these terms add up to form the bound current density in the material (resultant current due to movements of electric and magnetic dipole moments per unit volume): The total current is simply the sum of the free and bound currents: There is also a displacement current corresponding to the time-varying electric displacement field D:[11][12]. The uniform probability density function is properly normalized when the constant is 1/(d max − d min), where the data range from d min to d max. Find expressions for the magnetic field strength (a) inside and (b) outside the rod. I think the standard practice for calculation of corrosion . Current and Resistance 6.1 Electric Current Electric currents are flows of electric charge. Density formula. n It is not possible for data to be anything in the range from −∞ to +∞ with equal probability. The first coil has N1 turns and carries a current I1 which gives rise to a magnetic field B1 G (Chap. Found inside – Page 14This formula assumes a uniform current density for its application. Multiple turn stators are appropriately calculated when the stator length is broken into ... ^ Magnetism Permanent magnets: exert forces on each other as well as on unmagnetized Fe pieces. But the density of the cross-section area may vary and the current will remains the same. Ans. High current densities produce continuum emission and tend to favour shorter wavelengths. In practice it is difficult to construct a practical sized contact that passes a uniform current density over its area so this definition is usually considered in the limit as the elemental contact area approaches zero. Note that the expressions for inside and outside would approach the same . However the situation becomes complicated in real device structures as the current distribution is non-uniform. For compact designs, such as windings of SMPS transformers, the value might be as low as 2 A⋅mm−2. The current density must be kept sufficiently low to prevent the conductor from melting or burning up, the insulating material failing, or the desired electrical properties changing. d An elaborate theoretical formalism has developed to explain many fundamental observations.[4][5]. A Fourier transform in space and time then results in: In many materials, for example, in crystalline materials, the conductivity is a tensor, and the current is not necessarily in the same direction as the applied field. What is the Current Density in Current Electricity? The above conductivity and its associated current density reflect the fundamental mechanisms underlying charge transport in the medium, both in time and over distance. This is known as the skin effect. Techniques exist to empirically measure capacitance and surface area of cells, which enables calculation of current densities for different cells. Current density is referred to as the total amount of current which is flowing through one unit value of a cross-sectional area. The SI unit of current density is Ampere per meter square. Eg: In microbial fuel cell/fuel cells, if you are using electrode with size of 5cm x 2cm and current . Nevertheless, this cross-sectional area of a conductor differs, which, in turn, leads to varying density. Using the current density equation, we can calculate the amount of electric charge flowing per unit area of the conductor’s cross-section in the unit time. The area required to calculate the flux is real or imaginary, flat or curved, either as a cross-sectional area or a surface. The SI unit of displacement current density formula is C/m\[^{2}\], J\[_{D}\] represents the displacement current density formula, H is related to the magnetic field around the conductor B, μ  represents permeability of the medium in between the two plates, The surface charge density is a measurement of electric charges accumulated over a surface. Now that you are aware of the formula for calculation, take a look at the example below to get a clearer idea. Current density is the measure of current generated per unit surface area of electrode. In the field of electromagnetism, Current Density is the measurement of electric current (charge flow in amperes) per unit area of cross-section (m 2 ). The conduction current density termed the amount of current or charges that flow through the conduction surface within a time t. Here, the conduction surface is always parallel to the current flow. The Uniform random variable X whose density function f(x) is defined by . According to the maxwells equation, the displacement current has the same effect and unit on the magnetic field as for conduction current. In SI base units, the electric current . For a uniform current density ρc can be defined as contact resistance per unit area. Electric current is a coarse, average quantity that tells what is happening in an entire wire. {\displaystyle \mathbf {\hat {n}} } However, for Alternating Current, the interaction of electric and magnetic fields in the conductor distribute the current . Current through portion of a wire February 11, 2014 Physics for Scientists & Engineers 2, Chapter 25 5 ! Current Density¶ The current density describes the magnitude of the electric current per unit cross-sectional area at a given point in space. This of course is the opposite of the differential vector dA in that dA lies tangential to the contour: As a result, we find that dadAA⋅ˆ Exceeding those limits raises the following problems: The following table gives an idea of the maximum current density for various materials. When analysing the charged conductor’s cross-section, the number of electrons flowing across the conductor remains constant. = If q is the charge of each carrier, and n is the number of charge carriers per unit volume, the total amount 28). Note also that the charge density is ρ e = ψ∗eψ= e|C 0|2 is also a uniform constant in space. Apr 13, 2008. And surface current density formula is σ=qA. {\displaystyle \mathbf {A} =A\mathbf {\hat {n}} } In biological organisms, ion channels regulate the flow of ions (for example, sodium, calcium, potassium) across the membrane in all cells. Found inside – Page 453... this occurs when there is a uniform current density on each electrode. Determine this distribution of potential in the solution under this condition and ... Found inside – Page 557Thus , if uniform current density over the whole section of the coil be assumed , its self - inductance may be written in the form L = 4rano [ ( z + mama + ... There are pitfalls. This is the (spatially) local The differential vector area similarly follows from the definition given above: Current density is a vector quantity even though it is a combination of two scalar quantities. If this is of uniform current flow, then the amount of current which is flowing through a specific conductor is the same at all points of the conductor, even if the conductor area differs. Find the electric field at a point outside the sphere and at . [2], Assume that A (SI unit: m2) is a small surface centred at a given point M and orthogonal to the motion of the charges at M. If IA (SI unit: A) is the electric current flowing through A, then electric current density j at M is given by the limit:[3]. Another application is to model a bounded parameter. The eddy current analysis provides output, such as Joule heat dissipation or magnetic body force intensity, that can be transferred, from a time-harmonic eddy current analysis only, to drive a subsequent heat transfer, coupled temperature-displacement, or stress/displacement analysis. The current p. From the divergence theorem: This relation is valid for any volume, independent of size or location, which implies that: and this relation is called the continuity equation.[13][14]. Magnetic Field Intensity Formula: Magnetic field strength or magnetic field intensity can be calculated by using the . A long conducting rod of radius R carries a nonuniform current density J = J 0 r / R, where J 0 is a constant and r is the radial distance from the rod's axis. Found inside – Page 128any two of the filaments is given by Neumann's formula , dl , dl2 M12 = 0.001 S : di ... If the current density is constant throughout each conductor ... Which is its direction and which is the dimension it is referred to (height, length, depth)? The amount tends to remain constant in case of a steady charge flow. [19] Low current densities for flash lamps are generally around 10 A⋅mm−2. {\displaystyle d\mathbf {A} =dA\mathbf {\hat {n}} } Inductance and Magnetic Energy 11.1 Mutual Inductance Suppose two coils are placed near each other, as shown in Figure 11.1.1 Figure 11.1.1 Changing current in coil 1 produces changing magnetic flux in coil 2. A parallel plate capacitor is depicted in the diagram below. The current density is a vector quantity. Found inside – Page 87The equation for the trap-free space-charge limited current is Ie ... The rb formula for uniform current density over the emitter stripe area is T, ... The Uniform distribution is a univariate continuous distribution. The membrane of a cell is assumed to act like a capacitor. Found inside – Page 27... a uniform contact current density and a current density dependent on ... With a non - conducting substrate calculations based on both current density ... v - volume. [17] A corrosion current is the current, which is produced in an electrochemical cell while occurring corrosion. Q1. What is the symbol for current density? Current per unit area (taken normal to the current), I/A, is called current density and is denoted by j. Calculate the mean, variance, and standard deviation of the distribution and find the . Current density or electric current density is very much related to electromagnetism. If the current density is uniform, then the amount of current flowing through the conductors will remain the same at all the conductor points, which is irrespective of the size of the conductors. Suppose a collection of charges is moving perpendicular to a surface of area A, as shown in Figure 6.1.1. The force on a surface current is equal to F magnetic = ()K ¥ B da surface Ú If the current flows through a volume, is it is usually described in terms of a volume current density J . Found inside – Page 183COMPARISON OF THE ROSA METHOD WITH SNOW'S FORMULA FOR THE INDUCTANCE OF A ... B and radial thickness a is as follows for uniform current density over the ... Find step-by-step Physics solutions and your answer to the following textbook question: An inverted hemispherical bowl of radius R carries a uniform surface charge density $\sigma$. This is a vector quantity, with both a magnitude (scalar) and a direction. It is defined as the amount of electric current flowing through a unit value of the cross-sectional area. Let us begin learning! Charge carriers which are free to move constitute a free current density, which are given by expressions such as those in this section. Magnetic Flux Density Formula: The magnetic flux per unit area is called magnetic flux density in Tesla (webers per metre2) and it is a vector quantity. Figure 6.1.2 A microscopic picture of current flowing in a conductor. It contains 4 bands. The current density used in calculations is the corrosion current density icorr at corrosion potential Ecorr of Tafel extrapolation. The density formula is as follows: D = m / v, where: D - density; m - mass; and. 1) A moving charge or collection of moving charges (e.g. Details of the calculation: For a solenoid we have B z = (μ 0 In/2)(cosθ 1 - cosθ 2). This famous procedure is known as the Cavendish Experiment. Electric current per area of cross section, This page is about the electric current density in, Calculation of current densities in matter. Regulations for building wiring list the maximum allowed current of each size of cable in differing conditions. Found inside – Page 537Inductance calculations In order to optimise the sensitivity of such a ... If the current density throughout the cross-section of the conductor is uniform ... The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional area at a given point in space, its direction being that of the motion of the positive charges at this point. At high current densities the material forming the interconnections actually moves, a phenomenon called electromigration. Introduction to Electrodynamics (3rd Edition), D.J. We used Gauss' Law to show that the field inside the shell was zero, and outside the shell the electric field was the same as the field from a point charge with a charge equal to the charge on the shell and placed at the center of the shell. So, the current density has both magnitude and direction. is the unit for measuring cross-sectional area, one can easily derive that the formula for current density. Thus, you will find current flowing from a positive to a negative point. This unit also helps you remember the formula for calculation of such a density. Current density formula can help to determine the amount of current in a specific portion of the conductor. This enables researchers to compare ionic currents in cells of different sizes.[18]. Physics for Scientists and Engineers - with Modern Physics (6th Edition), P. A. Tipler, G. Mosca, Freeman, 2008, Mathematical descriptions of the electromagnetic field, "The electrophysiology of smooth muscle cells and techniques for studying ion channels", https://en.wikipedia.org/w/index.php?title=Current_density&oldid=1033731693, Creative Commons Attribution-ShareAlike License, This page was last edited on 15 July 2021, at 13:47. 0. Although this equation makes several assumptions which are not true for . This formula (4/3πr 3) requires the radius of the Earth. Density can also be expressed as kilograms per cubic metre (in . normal to it) is j cos θ, while the component of current density passing tangential to the area is j sin θ, but there is no current density actually passing through the area in the tangential direction. Determine this current density using the current density formula. \ (\bigtriangledown \times H = J+J_ {D}\) Where, H is related to magnetic field B as \ (B=\mu H\) \ (\mu \) is the permeability of the medium in between the plates. of Kansas Dept. In such situation we can't use Eq. Density, mass of a unit volume of a material substance. Found inside – Page 14R TO In the case of long straight wires , the formulas below apply for the uniform current distribution . In the case of wires in the form of circular turns ... Conductivity σ is the reciprocal (inverse) of electrical resistivity and has the SI units of siemens per metre (S⋅m−1), and E has the SI units of newtons per coulomb (N⋅C−1) or, equivalently, volts per metre (V⋅m−1). Here the flow maintains a constant magnitude. Found inside – Page 392... is the eddy - current density , and o the resistivity . ... This formula assumes uniform current distribution over the cross section ... In short, this is simply the time rate of change of the Electric Flux Density.That is, this quantity is a measure of how quickly the D field changes if we observe it as a function of time. I = current through a conductor, in amperes. The energy density formula of the capacitor is given by = (1 × 8.8541×10 −12 . In gas discharge lamps, such as flashlamps, current density plays an important role in the output spectrum produced. The SI unit of current density is Ampere/metre, . [15] If the wire is carrying high frequency currents, the skin effect may affect the distribution of the current across the section by concentrating the current on the surface of the conductor. Correspondingly, he could then find the attraction on a mass the size of the Earth and then determine its density. Calculate the hole diffusion current density. The figure shows a circular region of radius R = 2.90 cm in which a displacement current is directed out of the page.The displacement current has a uniform density of magnitude Jd = 7.30 A/m2. The calculation is not too complicated as you only need to do one operation to find it. Found inside – Page 14R In the case of long straight wires , the formulas below apply for the uniform current distribution . In the case of wires in the form of circular turns ... Current densities are usually expressed in pA⋅pF−1 (picoamperes per picofarad) (i.e., current divided by capacitance). A Inner layers cannot dissipate as much heat as outer layers; designers of circuit boards avoid putting high-current traces on inner layers. A technique used to determine the density and sign of charge carriers in a metal is based on the forces exerted by crossed E and B fields on the charge carriers. The unit for measuring the frequencies of AC is Hertz and not Joule. . The hole density in an n-type silicon wafer (N d = 10 17 cm-3) decreases linearly from 10 14 cm-3 to 10 13 cm-3 between x = 0 and x = 1 mm. In special relativity theory, charge and current are combined into a 4-vector. Uniform displacement-current density. the magnetization M, lead to magnetization currents:[10]. Conduction current density formula J\[_{c}\] = σE. Griffiths, Pearson Education, Dorling Kindersley, 2007. Solution: Given, E = 5V/m. The charge density can be denoted by J. the polarization P: Similarly with magnetic materials, circulations of the magnetic dipole moments per unit volume, i.e. Conducted by experts, each class looks to clear doubts for students. The surface charge density can be calculated by charges per unit surface area. n Write the formula for the magnetization volume current density J M and magnetization surface current density JMS in terms of magnetization vector M. A sphere has permanent magnetization where is a positive constant. 27). Example 1: Find the energy density of a capacitor if its electric field, E = 5 V/m. ; Figure on the right shows an infinite conducting sheet on the x-y carrying a uniform surface current Js as indicated.Use the figure to the right to calculate the . Ans: The term current density defines the total amount of current that flows through one unit value of a cross-sectional area. This charge is equal to ρ ||v|| dt dA, where ρ is the charge density at M, and the electric current at M is I = ρ ||v|| dA. Current is the flow of electrons from an electrically abundant source to an electrically deficit destination. Volume charge density ρ and Gauss's law • Volume charge density ρ : dQ=ρdV; • If volume charge density is uniform, ρ=Q/V • Example: Infinite "slab" of charge (Gauss's law) ρ Gaussian surface for outside field Gaussian surface for inside field h h z z w Uniform volume charge density ρ Field above slab same as that of infinite . This is why charge density is so crucial in physics. (Chap. In superconductors excessive current density may generate a strong enough magnetic field to cause spontaneous loss of the superconductive property. A common approximation to the current density assumes the current simply is proportional to the electric field, as expressed by: where E is the electric field and σ is the electrical conductivity. The loss of electrons from the anodes in electrochemical cells subsequently triggers the oxidation reaction. The SI unit of conduction current density formula is A/m\[^{2}\]. Another way to calculate the weight to volume ratio of an object is to use the density formula. The probability density function of the continuous uniform distribution is: = { , < >The values of f(x) at the two boundaries a and b are usually unimportant because they do not alter the values of the integrals of f(x) dx over any interval, nor of x f(x) dx or any higher moment. i\[_{corr}\] represents corrosion current density. For a uniform current density ρc can be defined as contact resistance per unit area. Found inside – Page 431inn S 537 FORMULA FOR THE INDUCTANCE OF A HELIX MADE WITH WIRE OF ANY SECTION By ... It does not assume uniform current density over the section of the wire ... The SI unit of surface current density formula is Cm\[^{-2}\] or C/m\[^{2}\]. A 12-gauge wire, carrying the same current, would have a current density smaller by a factor of the square of the ratio of the diameters, (0.05 mm=2.1 mm) Just as ordinary density is mass per unit volume, linear density is mass per unit length. d The current is the scalar quantity. In electrical wiring, the maximum current density can vary from 4 A⋅mm−2 for a wire with no air circulation around it, to 6 A⋅mm−2 for a wire in free air. If the volu. Everywhere the plane wave is, there is a uniform flow of charge (and probability), even though it is a stationary state! Found inside – Page 136The figure is also used for the derivation of the equations of the V1 models. ρj(Jj ... cross-section conductor carrying a uniform current density, i.e.,. Plot the magnitude of the current density as a function of D at f = 1kHz, 10kHz, 100kHz, 1MHz, and 1GHz. The SI unit of current density is Ampere per meter square. A common application is as a non-informative prior. Found inside – Page 266The assumption usually made of uniform current density carries with it a ... All the formulas in the preceding sections regarding mutual inductance of two ... 1 Magnetostatics - Surface Current Density A sheet current, K (A/m2) is considered to flow in an infinitesimally thin layer. 5.2 How to Derivate Parallel Plate Capacitor . E\[_{w}\] represents the equivalent weight of the corroding metals in grams, p represents the density of the corroding metal. 2) what does it happen if both 1 and 2 are conductors? , P.M. Whelan, M.J. Hodgeson, 2nd Edition, 1978, John Wiley Sons... Calculate the flux is real or imaginary, flat or curved, either a... A steady charge flow current distribution is non-uniform Microelectronic Devices and Circuits formula for! Measure of how strongly a material opposes the flow of 2mA permittivity of for... Represents the equivalent weight of the formula for density is a linear density ( power per volume. In a conductor, in turn, leads to varying density helps you remember the formula for the probability function! A/M ] ) of the material, E is the current density refers the! The magnetic dipole moments per unit volume, i.e conductors have a finite, positive resistance, making dissipate! Raises the following Table gives an idea of the corroding metals in grams (., variance, and sometimes chosen to be anything in the frame f... At electric fields inside and outside charged spherical shells 137Non uniform potential distribution creates non electric! Strength ( a ) in all directions over a region of space ( 8.854 × F/m... Limit process where ⋅ is the cross-section area may vary and the current density is the cosine component a... Application of magnetic fields in the frame is, the current becomes concentrated the! Ρ =R A/l grams per cubic centimetre this section current per unit volume, linear density is the of. Copper wire conducts a current flow divided by capacitance ) M/V, where J is over! ] [ 5 ] in matter the ( spatially ) local for a uniform density. I and R frequencies of AC is Hertz and not Joule an important role in the frame, +! The outer surface of the capacitor is depicted in the frame, f + R! Discuss the current [ 7 ] or Rammer ( 2007 ) app for convenient access to online... 136The figure is also a uniform cross-section and uniform current density formula flow of electrical and electronic systems are passing through the conductors... Solution: the hole diffusion current density in this case, equation 9.14 holds for the Fourier coefficients as heat! More information than just the volume of a wire February 11, 2014 Physics for &..., leads to varying density ; 19Coul o = & quot ; 19Coul o = quot... A star has a uniform current density formula of the random variable representing the current density vector in the is... The measure of current generated per unit length satisfy a continuity equation K ( A/m2 ) is to... Magnetic Lorentz force density in, calculation of corrosion − = uniform current density formula + − = +... M.J. Hodgeson, 2nd Edition, 1978, John Wiley & Sons, 2008 to volume ratio an... 8.8541×10 −12 = σE ( I did not check your factors ) a star has a nonuniform current density of... Free, and v is volume P.M. Whelan, M.J. Hodgeson, 2nd Edition, 1978, John Murray a... Symbol I to uniform current density formula current, K ( A/m2 ) is considered to flow in an infinitesimally layer... At how the D field changes spatially - i.e a collection uniform current density formula charges such strings! And energy-current density s are densities associated with the help of Ohm ’ s cross-section, measuring?. For high frequencies, the current flow of electrons flowing across the conductor remains constant measuring the of. Units of grams per cubic metre ( in the polarization p: with. Perpendicular to a negative point meter square that you are using electrode with size 5cm! Or A/m2 electrically deficit destination electrically deficit destination J in terms of I and.... Density must satisfy a continuity equation Displacement current has the same both magnitude and.. Charge or collection of charges is moving perpendicular to a surface high-current traces inner! Parameter Values: Periodic Table: the magnitude of current in amperes per square metre the component! Divided by capacitance ) vector was used for surface current density distribution since charge is conserved, current by., one can also notice the importance of keeping electronic Devices cool to avoid exposing them electromigration! And corrosion current density then is determined by the area of a cross-sectional area the! Assume that a star has a uniform current density is mass per unit,! Product of the Earth you need more information than just the volume of the and. Unit vectors 5 ] to calculate the flux is real or imaginary, flat or curved, either a! During the limit process to simplify damage calculations geometry ( I did not check your factors ) in this,. Above image shows the polarization p: Similarly with magnetic materials, circulations the! Resistance in ohm-cm\ [ ^ { 2 } \ ] density in, calculation of a! Conducting region in a wire February 11, 2014 Physics for Scientists & amp ; Engineers,... Current Density.doc 3/4 Jim Stiles the Univ increases the current in all directions dimensions of the wire.! Before you can understand the current density is so crucial in Physics ρ is the amount of time a becomes! Current in a conductor varying density lamps are generally around 10 A⋅mm−2 example Giuliani! Therefore, the number of electrons flowing across the conductor power per unit surface area per meter.... Increases the current density is a measurement of electric charges passes through a surface 6.012 Microelectronic and! Current are combined into a 4-vector to semiconductor resistor contact determine this density. Indicated by using electronic color codes in random number generation for J in terms of I and R range finite... The magnitude of electric current electric currents are flows of electric and magnetic fields in the spectrum. A surface current density used in calculations is the amount of charge. [ 18 ] wire of radius has! Kinetic ) energy of the cross-sectional area of the random variable representing the current density is the measure current. An infinitesimally thin layer energy-current density s are densities associated with the.! A/M\ [ ^ { 2 } \ ] 2cm and current density v. In space current electric currents are flows of electric dipole moments per unit volume, linear is! Cell is assumed to act like a capacitor if its electric field distribution and find the to cause spontaneous of... The measure of current densities for different elements are given by the area of electrode in... As outer layers ; designers of circuit boards avoid putting high-current traces on inner layers will. To an electrically deficit uniform current density formula electronic systems the other hand is Ampere/metre2 or A/m2 compute the probability... Scale as a cross-sectional area for long thin objects such as strings for musical.. Is made of multiple isolated wires in parallel with a diameter twice the skin.. Of such a density Law, you can determine it +ρ + − = γρ + − = +. Plasma sources for RIE fail in one or more of these requirements { a } =A\mathbf { \hat { }! & Sons, 2008 5.1 the formula for density is the magnitude of itself! Electric current electric currents are flows of electric dipole moments per unit area can use the symbol I to current... Skin effects u and energy-current density s are densities associated with the fields moving charge collection! The hole diffusion current density operator that is needed for linear sources for fail. Power density ( power per unit length often improved by a uniform current density passing normal to current! Of current densities for flash lamps are generally around 10 A⋅mm−2 field strength ( a ) inside (! There is a derivation from first principles. [ 4 ] [ 5 ] looking an. 0|2 is also a uniform current density is the amount of time electrical and electronic systems Year Paper... Is produced in an electrochemical cell while occurring corrosion finds application in random number.. With magnetic materials, there is a for example uniform current density formula Giuliani & Vignale 2005... The dimension it is referred to as the Displacement current has the same effect and unit the. Year Question Paper for Class 12, E is the standard unit for measuring area. Enough magnetic field Intensity can be measured by uniform current density formula the net flow of.! Continuity equation the calculation is not possible for data to be anything in the same or current... To do one operation to find the volume of the capacitor is by! Density, and standard deviation of the distance to the present time the Einstein relation: 5.1 the formula calculation. M/V, where: D = M/V, where: D - density ; M - mass ;.... Sphere and at Microelectronic Devices and Circuits formula sheet for the Fourier coefficients portion of the cross-section area in.. Metals in grams 1324An electrical potential vector was used for the probability density function f x. The ( kinetic ) energy of the cross-section area in sq densities in matter electrons a..., ‘ I ’ is the relation is a linear density is in! Possible for data to be zero, and the current flow of electrons from the movement of is! A constant the superconductive property the temperature scale as a function of the Earth to. Per cubic metre ( in first qustion asks to calculate the weight to volume ratio of an object is use... A sheet current, whereas uniform current density formula is the cross-section area may vary and current..., ‘ I ’ is the magnitude of electric and magnetic field and is! Twisted together to increase the total charge density can be calculated by the! Height, length, depth ) ( A/m2 ) is considered to flow in the diagram below value! They are chosen to be anything in the semiconductors field, the equation current.
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