The density of the direct electric current can be compared with the density of the gas flowing in the pipe under pressure. The current density is equal to the ratio of the current in amperes (A) to the cross sectional area of conductor in square millimeters (POS. 1 in the figure). From the conductor material, its value depends. Conductor cross section taken normal (perpendicular) to its longitudinal axis.
If, say, the wire has diameter D = 1 mm, the area of its cross section is S = 1/4(πD^2) = 3,1415/4 = 0.785 sq mm. If such a wire is flowing the current I is 5 A, then the density of j is equal to j = I/S = 5/0,785 = 6,37 A/sq. mm.
Though the value of the current density of the conductor material does not depend, in the technique it is chosen on the basis of its resistivity and length of the wire. The fact is that a large current density of a conductor it heats up, its resistance increases from this, and the power losses in the wiring or the coil increases.
However, if the wire is too thick, then all the wiring will be too expensive. Therefore, the calculation of household transactions are based on the so-called economic current density, the total long-term costs of electricity are minimal.
For residential wiring, the wire which is not very long, we take the value of economic density in the range of 6-15 A/sq. mm depending on the length of the wires. Copper wire with diameter of 1.78 mm (2.5 sq mm) PVC insulated, walled up with plaster coating, will withstand 30 or even 50 amps. But the consumption of power in the 5 kW density current in it will be (5000/220) = 23 A, and its density in the wiring – 9,2 A/sq. mm.
The economic current density in the power lines is much lower, in the range of 1-3,4 A/sq. mm. In electrical machines and transformers industrial frequency 50/60 Hz 1 to 10 A/sq. mm. In the latter case, it is calculated based on the allowable heating of the windings and the value of the electrical losses.
The current density of high frequencies (TV and radio signals, for example) calculated based on the so-called skin effect (skin – in English "skin"). Its essence is that the electromagnetic field pushes the current to the surface of the wire, so to obtain the desired density it is necessary to take the diameter of the wire more, and not to spend too much copper, to make it hollow, as a tube.
The skin effect is only important when transmitting large capacities. If, for example, to do the wiring of cable TV in the apartment are too thin coaxial cable, the losses in it due to the skin effect in the inner wire may be too long. Analogue channels will be ruffle, and a digital – to crumble into squares.
The depth of the skin effect depends on frequency and current density thus falls gradually to zero at the center of the wire. A technique to simplify the calculations, the depth of the skin surface considered where the current density decreases 2.72 times compared to the surface (POS. 2 in the figure). The value of 2.72 is shown in engineering electrodynamics from the ratio of electric and magnetic constant, which facilitates the calculations.
The bias current is quite a complex concept of electrodynamics, but thanks to his alternating current passes through the capacitor, and the antenna radiates the signal into air. The bias current also has its density, but to define it is not so easy.
Even in a very good capacitor the electric field is slightly "sticks" to the sides between the plates (POS. 3 in the figure), so to be crossed by the bias current surface should be given some Supplement. For a capacitor its value can still be neglected, but when talking about the antenna, then there is this virtual traversed by the bias current of the surface means everything.
To find the density of the bias current, it is necessary to solve complex equations of electrodynamics or to produce a computer simulation of the process. Fortunately, for many cases of engineering practices to know its value is not required.
If, say, the wire has diameter D = 1 mm, the area of its cross section is S = 1/4(πD^2) = 3,1415/4 = 0.785 sq mm. If such a wire is flowing the current I is 5 A, then the density of j is equal to j = I/S = 5/0,785 = 6,37 A/sq. mm.
The values of the current density in the technique
Though the value of the current density of the conductor material does not depend, in the technique it is chosen on the basis of its resistivity and length of the wire. The fact is that a large current density of a conductor it heats up, its resistance increases from this, and the power losses in the wiring or the coil increases.
However, if the wire is too thick, then all the wiring will be too expensive. Therefore, the calculation of household transactions are based on the so-called economic current density, the total long-term costs of electricity are minimal.
For residential wiring, the wire which is not very long, we take the value of economic density in the range of 6-15 A/sq. mm depending on the length of the wires. Copper wire with diameter of 1.78 mm (2.5 sq mm) PVC insulated, walled up with plaster coating, will withstand 30 or even 50 amps. But the consumption of power in the 5 kW density current in it will be (5000/220) = 23 A, and its density in the wiring – 9,2 A/sq. mm.
The economic current density in the power lines is much lower, in the range of 1-3,4 A/sq. mm. In electrical machines and transformers industrial frequency 50/60 Hz 1 to 10 A/sq. mm. In the latter case, it is calculated based on the allowable heating of the windings and the value of the electrical losses.
On the density of high frequency current
The current density of high frequencies (TV and radio signals, for example) calculated based on the so-called skin effect (skin – in English "skin"). Its essence is that the electromagnetic field pushes the current to the surface of the wire, so to obtain the desired density it is necessary to take the diameter of the wire more, and not to spend too much copper, to make it hollow, as a tube.
The skin effect is only important when transmitting large capacities. If, for example, to do the wiring of cable TV in the apartment are too thin coaxial cable, the losses in it due to the skin effect in the inner wire may be too long. Analogue channels will be ruffle, and a digital – to crumble into squares.
The depth of the skin effect depends on frequency and current density thus falls gradually to zero at the center of the wire. A technique to simplify the calculations, the depth of the skin surface considered where the current density decreases 2.72 times compared to the surface (POS. 2 in the figure). The value of 2.72 is shown in engineering electrodynamics from the ratio of electric and magnetic constant, which facilitates the calculations.
The density of the bias current
The bias current is quite a complex concept of electrodynamics, but thanks to his alternating current passes through the capacitor, and the antenna radiates the signal into air. The bias current also has its density, but to define it is not so easy.
Even in a very good capacitor the electric field is slightly "sticks" to the sides between the plates (POS. 3 in the figure), so to be crossed by the bias current surface should be given some Supplement. For a capacitor its value can still be neglected, but when talking about the antenna, then there is this virtual traversed by the bias current of the surface means everything.
To find the density of the bias current, it is necessary to solve complex equations of electrodynamics or to produce a computer simulation of the process. Fortunately, for many cases of engineering practices to know its value is not required.