Units of inductance, voltage-current relationship, time constant and impedance

2025-03-22

Units of inductance

Inductance reflects the ability of a device to resist current changes. This "resistance" is reflected in the induction current and induced electromotive force (also called: back electromotive force, Back EMF) generated on the inductor.

The unit of inductance is Henry, and the symbol is L. The definition of L=1 Henry is: the current changes at a rhythm of 1 ampere per second (1A/s). If the voltage of the induced electromotive force generated on the inductor is 1V, this inductance is 1 Henry.

In radio and communication equipment, the common inductance unit is nH (nanohenry), which can cope with MHz-level current changes; in power supplies and power supply equipment, the common inductance unit is μH (uH, microhenry), which can cope with KHz-level current changes; in audio equipment, the common inductance unit is mH (millihenry), which can cope with hundreds of Hz to 2KHz-level current changes.

In the process of resisting current changes, the inductor is accompanied by the conversion of electrical energy and magnetic energy. The larger the capacity of the inductor, the greater the energy that can be converted and stored.

Changes in voltage and current on the inductor

Let's take a look at the relationship between the voltage and current on the inductor: V=-L*di/dt

This formula reflects that the voltage of the induced electromotive force on the inductor is related to the speed of current change.

When L is constant, the faster the current changes, the higher the induced electromotive force voltage generated. Especially when the circuit switch is opened or closed, the instantaneous change of current can cause sparks to appear at the circuit switch (sparks can only be generated by breaking through the air, at least tens of thousands of volts, the instantaneous voltage is very high, the duration is short, but the energy is not necessarily large).

We build a circuit consisting of an inductor, a resistor, and a power supply (periodic square wave), as shown below:

A voltmeter is connected in parallel to each device to facilitate viewing the waveform. In particular, the current on the entire circuit can be inferred through the voltage on the resistor (Ohm's law). The power supply uses a periodic square wave of Max 10V, Min 0V, and 100Hz.

Let's take a look at the changes in the voltage and current waveforms on the inductor:

Among them, the green waveform represents the change in the power supply voltage; the yellow waveform represents the change in the inductor voltage; the blue waveform represents the change in the resistor voltage, which also reflects the change in the current in the entire circuit.

When the power supply changes from 0V->10V, the voltage of the inductor generates a positive pulse (voltage mutation), and the polarity of this pulse is opposite to the polarity of the power supply voltage. Since the inductor voltage weakens the influence of the power supply voltage, the current does not suddenly increase. The current of the entire circuit starts from 0A and gradually increases (the current cannot change suddenly) until it reaches a steady state.

When the power supply changes from 10V->0V, the voltage of the inductor generates a negative pulse (voltage mutation), and the polarity of this pulse is the same as the polarity of the power supply voltage. Since the inductor voltage continues the influence of the power supply voltage, the current does not suddenly decrease. The current of the entire circuit starts from 1A (10V/10Ω) and gradually decreases (the current cannot change suddenly) until it reaches a steady state.

This is consistent with what we said in the previous article that the inductor is an inertial device in the field of electromagnetics. It does not like the current to change and always uses its own energy to maintain the original state of the current.

Note that this circuit intentionally does not have a switch device. Even when the power supply voltage is at least 0V, the entire circuit is still conducting. However, if a switch is placed in the circuit, the performance when the switch is disconnected is different from when the power supply is 0V. We will analyze this later. You can imagine that the inductor is an inertial device for the current. If the circuit is suddenly disconnected and the current has no loop, what will happen?

Time constant of inductor

In the LR circuit, in response to changes in external excitation (DC), it takes a certain process for the voltage and current of the inductor to reach a stable state, and its waveform conforms to exponential changes:

Time constant τ=L/R. After 5 τ, the voltage and current of the inductor tend to stabilize, especially for DC, when the inductor is equivalent to a short circuit and the current reaches the maximum Imax=V/R.

In the process of reaching a steady state, the inductor is also storing energy (converting electrical energy into magnetic energy, corresponding to the above-mentioned excitation power supply from 0V->10V) or releasing energy (converting magnetic energy into electrical energy, corresponding to the above-mentioned excitation power supply from 10V->0V). Therefore, this constant is also called the charge and discharge time constant.

Impedance of inductor - inductive reactance

Like capacitors, impedance is needed to measure the performance of inductors under different frequency excitations. In particular, for pure inductive circuits, impedance is inductive reactance.

The formula for calculating inductive reactance is X=2π*f*L. The higher the frequency, the greater the inductive reactance.

For example, what will happen if we increase the power supply excitation in Figure 2 from 100Hz to 1KHz?

In this circuit, as the frequency increases, it means that the inductor impedance becomes larger, so more voltage can be allocated to the inductor, while the voltage allocated to the resistor becomes less. From another perspective, if the resistor is a load, isn't this a step-down circuit?

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