What alternating-current such pure resistance?

The size and initial phase of the alternating current created by alternating voltage depend not only on the size of resistance forming the electric circuit but also on inductance and the capacity of this chain.

Активное сопротивление в цепи переменного тока

Pure resistance in the alternating current circuit.

Strictly speaking, any electric circuit has, except resistance, also inductance and capacity. If on the conductor there passes current, then around it magnetic field is excited, i.e. the inductance phenomena take place. Current arises under the influence of electric field on charges , therefore, the conductor has to have the capacity as in the dielectric environment around it there is the shift flow.

However in some cases the relative role of two of three R, L, S parameters in the electric circuit is almost insignificant. It allows to consider the similar chain as having only resistance, either only inductance, or only capacity. We will consider in turn conditions in three such simplest alternating current circuits.

In the chain containing only resistance of, sinusoidal tension of u = Um sin? t of the source of the electric power creates current:

 i = u: r = (Um: r) sin? t

As r resistance does not depend on time, in this chain current matches on the phase tension (fig. 1) and changes also sinusoidalno:

i = Im sin? t


Im = Um: r

Кривые мгновенных значений напряжения и тока в цепи,содержащей только сопротивление r

The drawing 1 Curves of instantaneous values of tension and the circuit current, r containing only resistance.

Having separated the last expression on , we will receive the Ohm's law formula for the operating values of tension and current:

I = U: r

Apparently from the formula, this law for the alternating current circuits containing only r resistance has the same appearance, as well as the Ohm's law for the direct-current circuit.

In the alternating current circuit resistance of r is called pure resistance. This resistance in which the electric power will be transformed to other form (in warmth, etc.). It can significantly differ from r resistance at the direct current. Resistance for the direct current is called ohmic to distinguish it from pure resistance for alternating current.

The difference between active and ohmic resistance is caused by the variety of reasons. One of them - the skin effect, alternating-current partial replacement in blankets of the conductor. The more the alternating-current frequency, the this replacement is more considerable. Because of the skin effect resistance of r is shown already significantly big, than calculated on the formula:

r =? (l: S)

The skin effect is created by the fact that the alternating magnetic field induces in external layers of the conductor the smaller EMF of the self-induction, than in its internal part. Especially strongly skin effect increases the pure resistance of steel wires. With the industrial frequency the skin effect significantly influences the pure resistance of copper and aluminum wires only at big sections of wires (over 25 sq. mm).

Except the skin effect, losses of energy in the variation electromagnetic field of the chain from the hysteresis and whirling currents can cause big increase in pure resistance of the electric circuit.

  1. Luann Rebeiro

    The necessary and professionally stated things. It should be known too.

    To answer
    • admin

      These are questions of electrical equipment and to have about it though some representation, of course is necessary.

      To answer
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