Understanding Inductance- Khan Academy Physics Guide
What Inductance Actually Is
Inductance is the property of a conductor that opposes changes in current flow. That's the blunt definition. When current tries to increase or decrease through a coil, the magnetic field it creates fights back.
Every conductor has this property, but coils amplify it. More turns = more inductance. It's that simple.
Self-Inductance vs Mutual Inductance
Self-inductance happens when a changing current in a coil induces its own opposing EMF. The coil essentially fights itself.
Mutual inductance occurs when a changing current in one coil induces EMF in a nearby coil. Transformers work on this principle. No physical contact needed—just shared magnetic flux.
The induced EMF in both cases follows Faraday's Law:
EMF = -L × (dI/dt)
The negative sign represents Lenz's Law—the induced current always opposes the change that created it.
The Inductance Equation
For a solenoid (long coil), inductance is:
L = (μ₀ × N² × A) / l
- L = inductance in Henries
- N = number of turns
- A = cross-sectional area in m²
- l = coil length in meters
- μ₀ = permeability of free space (4π × 10⁻⁷ H/m)
Notice N is squared. Doubling the turns quadruples the inductance. This matters when designing circuits.
What Determines Inductance
Three factors control how much inductance you get:
- Coil geometry — More turns and larger area increase L
- Core material — Iron or ferrite cores concentrate magnetic flux, raising inductance dramatically
- Coil length — Longer coils reduce inductance per turn
Types of Inductors
Inductors aren't one-size-fits-all. Different constructions serve different purposes:
| Type | Core Material | Typical Use | Characteristics |
|---|---|---|---|
| Air core | None (air) | RF circuits, high frequency | Low inductance, no core losses |
| Iron core | Iron | Power supplies, audio | High inductance, saturation risk |
| Ferrite core | Ferrite | SMPS, EMI filtering | High frequency efficiency |
| Toroidal | Various | Power conditioning | Low EMI, efficient field containment |
Energy Stored in an Inductor
Inductors store energy in their magnetic field. The formula:
W = ½ × L × I²
Energy increases with the square of current. Double the current, quadruple the stored energy. This matters for safety when discharging large inductors—they can dump serious energy fast.
RL Time Constant
Inductors don't change current instantly. They resist changes, and the time constant τ (tau) describes how fast:
τ = L / R
After one τ, current reaches 63% of its final value. After 5τ, it's essentially settled at 99%.
This behavior makes inductors useful for filtering and smoothing, but it also means circuits don't respond instantly to changes.
How Inductors Behave in Circuits
Inductors have frequency-dependent behavior:
- DC (0 Hz) — Inductor acts like a short circuit (after settling)
- Low frequency — Low reactance, allows current through
- High frequency — High reactance, blocks signal
Reactance (opposition to AC) follows:
X_L = 2πfL
Double the frequency, double the reactance. This is why inductors work as low-pass filters—they let DC through and block high-frequency noise.
Getting Started: Solving Basic Inductance Problems
Here's the process for typical physics problems:
Step 1: Identify Known Variables
Extract N, A, l, and core type from the problem. Units matter—convert everything to meters and m² before calculating.
Step 2: Calculate or Look Up μ
For air cores, use μ₀. For magnetic cores, multiply by relative permeability (μr). Iron might have μr of 5,000 or more—this makes a massive difference.
Step 3: Apply the Formula
L = (μ × N² × A) / l. Plug in numbers. Check your units.
Step 4: Find Reactance or Energy as Needed
Depending on what's asked, calculate X_L = 2πfL or W = ½LI². Match the formula to the question.
Example
A solenoid has 500 turns, length 0.1m, area 0.0001 m², air core.
L = (4π × 10⁻⁷ × 500² × 0.0001) / 0.1
L = 0.000314 H = 314 μH
At 60 Hz: X_L = 2π × 60 × 0.000314 = 0.119 Ω
Common Applications
Inductors show up everywhere once you know where to look:
- Power supplies — Energy storage in switching regulators
- Filters — Block or pass specific frequencies
- Transformers — Step voltage up or down via mutual inductance
- Ignition systems — Generate high voltage spikes
- RL circuits — Time delays and transient response
What Khan Academy Gets Right (and What to Supplement)
Khan Academy's inductance coverage is solid for conceptual understanding. The videos explain Faraday's Law clearly and walk through the math step-by-step. Good starting point.
Where it falls short: real-world applications and circuit behavior get less attention. For practical design work, you'll need additional resources covering inductor selection, saturation limits, and parasitic capacitance.
Use Khan Academy to build intuition. Supplement with circuit analysis textbooks or manufacturer datasheets for practical implementation details.