RL Circuits
An RL circuit is an electrical circuit containing a resistor (R) and an inductor (L). These circuits are widely used for current limiting, filtering, timing, relay protection and power electronics. Unlike a purely resistive circuit, an RL circuit does not allow current to change instantly because the inductor opposes changes in current by storing energy in its magnetic field.
Basic RL Circuit
The simplest RL circuit consists of a resistor and an inductor connected in series to a DC voltage source.
+V ā [R] ā [L] ā GND
When power is applied, the resistor limits the current while the inductor causes the current to rise gradually instead of instantly.
How an RL Circuit Works
When the supply voltage is first applied, the inductor generates a voltage that opposes the increase in current. As the magnetic field builds, this opposing voltage decreases and the current gradually rises until the circuit reaches a steady state.
When the supply is removed, the collapsing magnetic field attempts to keep the current flowing, producing a voltage that can be much higher than the supply voltage.
Time Constant
The speed at which current rises or falls is determined by the time constant (Ļ).
Ļ = L / R
| Symbol | Description |
|---|---|
| Ļ | Time constant (seconds) |
| L | Inductance (henries) |
| R | Resistance (ohms) |
After one time constant, the current reaches approximately 63% of its final value. After about five time constants, it has reached more than 99% of its final value.
Current Rise After Switching On
| Elapsed Time | Approximate Current |
|---|---|
| 1Ļ | 63% |
| 2Ļ | 86% |
| 3Ļ | 95% |
| 4Ļ | 98% |
| 5Ļ | More than 99% |
Current Decay After Switching Off
When power is removed, the magnetic field collapses and the stored energy is released. The current decreases exponentially until it reaches zero.
| Elapsed Time | Remaining Current |
|---|---|
| 1Ļ | 37% |
| 2Ļ | 14% |
| 3Ļ | 5% |
| 5Ļ | Less than 1% |
Energy Stored in the Inductor
While current flows, the inductor stores energy in its magnetic field.
Energy = Ā½ Ć L Ć IĀ²
When the circuit is switched off, this energy must be safely dissipated or redirected.
Applications of RL Circuits
| Application | Purpose |
|---|---|
| Relay Circuits | Control current and switching behaviour. |
| Solenoids | Electromagnetic actuation. |
| Power Supplies | Filtering and current smoothing. |
| Motor Drives | Current control. |
| Audio Equipment | Signal filtering. |
| Industrial Automation | Control and protection. |
Protecting RL Circuits
When current through an inductor is interrupted, the resulting voltage spike (back EMF) can damage switches, relays and semiconductor devices.
| Protection Method | Purpose |
|---|---|
| Flyback Diode | Protects DC relay coils. |
| RC Snubber | Reduces switching spikes. |
| TVS Diode | Clamps high-voltage transients. |
| MOV | Protects AC-powered circuits. |
Testing RL Circuits
- Measure resistance with a multimeter.
- Measure inductance using an LCR meter.
- Observe current rise and decay with an oscilloscope.
- Check for excessive heating.
- Inspect switching devices for damage caused by back EMF.
Common Faults
| Fault | Possible Cause |
|---|---|
| Open Inductor | Broken winding. |
| Shorted Turns | Insulation failure. |
| Burnt Resistor | Overcurrent. |
| Damaged MOSFET or Transistor | Back EMF spike. |
| Slow Relay Operation | Incorrect component values. |
Worked Example
Given:
L = 100 mH R = 50 Ī©
The time constant is:
Ļ = L / R Ļ = 0.1 / 50 Ļ = 0.002 s Ļ = 2 ms
After approximately 10 ms (5Ļ), the current has reached more than 99% of its final value.
Interesting Facts
- Relay coils are practical examples of RL circuits.
- Inductive kickback can generate voltages much higher than the supply voltage.
- The time constant determines how quickly an RL circuit responds to changes.
- Many motor controllers rely on RL behaviour to regulate current.
- Flyback diodes are commonly used to protect transistors driving relay coils.
Key Points
- An RL circuit contains a resistor and an inductor.
- The inductor opposes changes in current.
- The time constant equals inductance divided by resistance (Ļ = L/R).
- Current rises and falls exponentially.
- Protection against back EMF is essential in switching applications.