Inductor components in sinusoidal AC circuits

Linear non-time-varying inductance elements are an important and basic element in circuits. In actual circuits, we often encounter inductance coils made of wires. When current passes through a linear inductance element with self-inductance L , if the voltage across the inductance element is consistent with the reference direction of the current, as shown in Figure 3-5-1, then according to Lenz's law, the relationship between current and voltage is:

(3-5-1)

Where L is the inductance value in Henry (H).

Figure 3-5-1

When the current passing through the inductor is a sinusoidal alternating current, that is , substituting into the above formula, the voltage across the inductor element is

(3-5-2)

It can be seen from the above formula that the voltage at the inductor terminal is a sinusoidal quantity with the same frequency as , and the phase of the voltage leads the current period, that is or .

From formula (3-5-2), we can get that the effective value of the inductor current and the effective value of the inductor terminal voltage are related by

(3-5-3)

In the formula, the self-inductance of the inductor coil is called inductive reactance, which has the same dimension as resistance. When the unit of inductance L is H and the unit of angular frequency is , the unit of inductive reactance is H. Inductive reactance is generally represented by the letter , that is,

(3-5-4)

Example 3-5-1: A coil with negligible resistance has an inductance value of . If the current flowing through it is , what is the coil voltage ? If the current frequency is , calculate the coil terminal voltage again .

Solution: Assume that the current phase is , when the frequency is , the inductive reactance

The voltage vector can be obtained from formula 3-5-5:

Yes .

When the frequency , the inductive reactance , the voltage vector

, voltage instantaneous type .