Inductance Formula
Learn the inductance formula V = L(dI/dt) and how inductors combine in series and parallel.
Key to understanding electromagnetic circuits.
The Formula
An inductor opposes changes in current flowing through it.
The voltage across an inductor is proportional to the rate at which the current is changing.
The SI unit of inductance is the Henry (H).
Variables
| Symbol | Meaning |
|---|---|
| V | Voltage across the inductor (Volts, V) |
| L | Inductance (Henrys, H) |
| dI/dt | Rate of change of current (Amperes per second, A/s) |
Series and Parallel Rules
Inductors in series (total inductance increases):
Inductors in parallel (total inductance decreases):
Example 1
A 0.5 H inductor has current changing at 4 A/s. What voltage is induced?
V = L × (dI/dt)
V = 0.5 H × 4 A/s
V = 2 V
Example 2
Two inductors, 10 mH and 40 mH, are connected in parallel. Find the total inductance.
1/L_total = 1/L₁ + 1/L₂
1/L_total = 1/10 + 1/40
1/L_total = 4/40 + 1/40 = 5/40
L_total = 40/5
L_total = 8 mH
When to Use It
Use the inductance formula when you need to:
- Calculate the voltage produced by a changing current in a coil
- Design transformers, motors, and electromagnetic devices
- Analyse RL (resistor-inductor) transient circuits
- Build filters and oscillator circuits
Energy stored in an inductor is E = ½LI².
Inductor combination rules follow the same pattern as resistors: they add directly in series and use the reciprocal formula in parallel.
Key Notes
- Fundamental formula: V = L × dI/dt: An inductor opposes changes in current — the faster the current changes, the higher the voltage developed across it. A steady DC current through an inductor produces zero voltage; inductors are essentially wires for DC.
- Inductive reactance: X_L = 2πfL: The AC "resistance" of an inductor increases linearly with frequency. At high frequencies, an inductor blocks current effectively. At low frequencies (and DC), it passes current freely. This makes inductors ideal for low-pass filters.
- Energy storage: E = ½LI²: Inductors store energy in their magnetic field — analogous to a capacitor storing energy in an electric field (E = ½CV²). When current is suddenly interrupted, the inductor releases this energy as a high-voltage spike (the cause of flyback in relay and motor circuits).
- Series and parallel combinations: Inductors in series: L_total = ΣLᵢ (like resistors). In parallel: 1/L_total = Σ(1/Lᵢ). This is the opposite of capacitors. Mutual inductance (transformer coupling) adds complexity in series combinations.
- Applications: Inductors are used in transformers, power supply chokes (filtering switching noise), radio tuning circuits (with capacitors in LC resonant circuits), motor windings, and electromagnetic relays.