Inductor Charging (Current Build-Up)
Although the term "charging" is commonly used, an inductor does not charge in the same way as a capacitor. Instead, when a voltage is applied, the current through the inductor increases gradually while energy is stored in its magnetic field. This gradual increase in current is known as the current build-up or energising process.
What Happens When Voltage Is Applied?
When a DC voltage is first applied, the inductor immediately opposes the change in current by generating a voltage known as back electromotive force (back EMF).
As the magnetic field builds, the opposing voltage decreases and the current gradually rises until it reaches its steady-state value.
Stages of Current Build-Up
| Stage | What Happens |
|---|---|
| Power Applied | Current starts at zero. |
| Magnetic Field Forms | Current increases gradually. |
| Current Rising | Back EMF becomes smaller. |
| Steady State | Current reaches its final value. |
Current Build-Up
The current does not rise linearly. Instead, it follows an exponential curve determined by the RL time constant.
Ļ = L / R
where:
| Symbol | Meaning |
|---|---|
| Ļ | Time constant |
| L | Inductance (H) |
| R | Total circuit resistance (Ī©) |
Current After Each Time Constant
| Time | Current |
|---|---|
| 0 | 0% |
| 1Ļ | 63.2% |
| 2Ļ | 86.5% |
| 3Ļ | 95.0% |
| 4Ļ | 98.2% |
| 5Ļ | 99.3% |
Energy Storage
As current increases, the magnetic field stores energy.
Energy = Ā½ Ć L Ć IĀ²
This energy remains stored while current flows through the inductor.
What Happens at Steady State?
After several time constants, the current becomes constant. Under DC conditions, the magnetic field is fully established and the inductor behaves almost like a short circuit, limited mainly by its winding resistance (DCR).
Factors Affecting Charging Time
| Factor | Effect |
|---|---|
| Higher Inductance | Slower current build-up. |
| Lower Inductance | Faster current build-up. |
| Higher Resistance | Shorter time constant. |
| Lower Resistance | Longer time constant. |
| Higher Supply Voltage | Higher final current (for a fixed resistance). |
Applications
| Application | Purpose |
|---|---|
| Relay Circuits | Magnetic field generation. |
| Solenoids | Mechanical movement. |
| Motor Controllers | Current regulation. |
| Switch-Mode Power Supplies | Energy storage. |
| Electromagnets | Controlled magnetic fields. |
Worked Example
Given:
L = 50 mH R = 10 Ī©
Calculate the time constant.
L = 0.05 H Ļ = L / R Ļ = 0.05 / 10 Ļ = 0.005 s Ļ = 5 ms
After approximately 25 ms (5Ļ), the current has reached more than 99% of its final value.
Common Mistakes
- Thinking an inductor stores electrical charge like a capacitor.
- Assuming current reaches its maximum instantly.
- Ignoring the winding resistance (DCR).
- Confusing current build-up with capacitor charging.
- Ignoring back EMF during switching.
Interesting Facts
- An inductor stores energy in a magnetic field, not as electric charge.
- Current through an ideal inductor cannot change instantaneously.
- Relay coils and solenoids demonstrate current build-up every time they are energised.
- Large inductors require more time to reach full current than small inductors.
- The charging process follows an exponential curve rather than a straight line.
Key Points
- Inductors do not charge like capacitors.
- Applying voltage causes current to build gradually.
- The magnetic field stores the energy.
- The RL time constant determines the charging speed.
- After about five time constants, the current is essentially at its final value.