5.4. Alternating current. The Ohm law for alternating current

Forced electric oscillations can be considered as flow of alternating current (ac) under the action of external EMF in a closed electric circuit which consists of a capacitor, an inductance coil, and an ohmic resistance. The current changes according to harmonic law its amplitude is

(2.58)

Denominator of equation (2.58)

(2.83)

is cold total resistance or impedance.

Equation (2.58) is cold the Ohm law for alternating current.

If an electric circuit has an ohmic resistance only, equation (2.58) turns into

(2.84)

Comparison of equation (2.84) with (2.58) shows that disregard of an inductance coil means that but disregard of a capacitor means that (short-circuited capacitor).

If an electric circuit has an inductance coil only ( ), equations (2.58) and (2.60) give

(2.85)

Value

(2.86)

is cold inductive reactance.

Inductive reactance (2.86) is used for creation of chokes. They represent wire coils which are entered in an electric circuit where alternating current flows for regulation the current intensity. Chokes have advantage in comparison with rheostats as the increase of their resistance is not accompanied by increase of Joule heat, and so, useless Joule loss of energy is absent. Besides, inductive reactance exists only for alternating currents (inductance does not make resistance to direct current), chokes allow to divide direct and alternating currents.

According to (2.86) inductive reactance grows with increase of frequency; therefore, for very big frequencies even small inductance represents significant resistance. Following experiment proves it. Let a thick copper rod of 5 mm diameter and 1 m length has the form of an arch abcde. The rod is connected to a EMF source which frequency (Fig. 2.12). An incandescent lamp is connected to the arc in parallel. The copper arc resistance for direct current is the lamp resistance is 100 Therefore, the arc short-circuits the lamp.

But for alternating current, the arc has inductive reactance If , the arc resistance becomes very large and the current totally flows through the lamp giving rise to its bright shining.

Fig. 2.12

If an electric circuit has a capacitance only ( ), equations (2.58) and (2.60) give

(2.87)

and Value

(2.88)

is cold capacitive resistance.

Direct current cannot flow through a capacitor.

Equation (2.88) can be easy check up experimentally if we make an electric circuit which contains the variable capacitor and incandescent lamp connected in series, and connect the circuit to an alternating current source. Changing the capacity shows that the larger is the capacity the brighter is the lamp shining and, hence, stronger is the current. Therefore, a capacitor resistance is inversely proportional to its capacity. Equation (2.88) shows that for alternating current at very high frequencies even small capacities have absolutely insignificant resistance. An interesting fact confirms it. Experimenter (Fig. 2.13) stands on an isolated bench with glass legs and touches through a conductor a lamp.

Fig. 2.13

The second contact of the lamp is connected to a high-voltage source of an alternating current with frequency ; the other contact of the source earthed. It is obvious, that for direct current the electric circuit is open. It is broken off by the isolated bench. However, the lamp is brightly shining. It means that the body of the experimenter and the ground represent a capacitor plates; alternating current flows through the capacitor. Therefore, the electric circuit that is open for a direct current appears closed for alternating current. As the current frequency is very high, the capacitor resistance becomes so small, that relatively strong current can flow in the circuit.

If an electric circuit has no ohmic resistance ( ), equation (2.58) changes into

(2.89)

Value is cold reactance.

We have considered different variants of electric circuits connected to external alternating EMF. All above mentioned equations are true for an electric circuit sections if instead of the EMF equation we take the equation for voltage across the section