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Inductance Calculator

Calculate inductive reactance, voltage across inductor, and stored energy with interactive visualization

Parameters

Hⓘ
Inductance of the inductor
Hzⓘ
Frequency of AC signal
Aⓘ
Current through the inductor
Inductance Analysis
Enter values to calculate reactance, voltage, and energy

Calculated Values

Inductive Reactance:
37.6991;Ω37.6991;Ω
Voltage across Inductor:
37.6991;V37.6991;V
Stored Energy:
0.0500;J0.0500;J
Reactance at 1kHz:
628.3185;Ω628.3185;Ω

Examples

Example 1: Household Inductor

A 0.1H inductor at 60Hz with 1A current.

  • Inductive Reactance: 37.737.7
  • Voltage across Inductor: 37.737.7
  • Stored Energy: 0.050.05

Example 2: Audio Inductor

A 1mH inductor at 1kHz with 0.5A current.

  • Inductive Reactance: 6.286.28
  • Voltage across Inductor: 3.143.14
  • Stored Energy: 0.0001250.000125

Example 3: Power Inductor

A 10H inductor at 50Hz with 10A current.

  • Inductive Reactance: 3141.63141.6
  • Voltage across Inductor: 3141631416
  • Stored Energy: 500500

Inductance and Inductive Reactance

Inductance is a property of electrical circuits that opposes changes in current. An inductor stores energy in its magnetic field when current flows through it. The unit of inductance is the henry (H), named after Joseph Henry.

Inductive reactance (Xₗ) is the opposition that an inductor offers to alternating current. It is calculated as Xₗ = 2πfL, where f is the frequency and L is the inductance. Unlike resistance, reactance depends on frequency - higher frequencies result in higher reactance.

In an AC circuit, the voltage across an inductor leads the current by 90 degrees. The voltage is given by V = XₗI = 2πfLI. This phase relationship is crucial for understanding AC circuit behavior.

The energy stored in an inductor is given by E = ½LI², where L is the inductance and I is the current. This energy is stored in the magnetic field and can be released when the current changes.

Inductors are used in filters, transformers, and energy storage applications. They are essential components in power supplies, audio equipment, and many electronic devices.

Key Concepts

  • Inductance (L): Property opposing current changes, measured in henries (H)
  • Inductive Reactance: Xₗ = 2πfL (frequency-dependent opposition)
  • Voltage across Inductor: V = XₗI = 2πfLI
  • Stored Energy: E = ½LI² (energy in magnetic field)
  • Phase Relationship: Voltage leads current by 90°
  • Frequency Dependence: Higher frequency = higher reactance

Real-World Applications

  • Power Supplies: Filtering and energy storage
  • Audio Equipment: Crossover networks and filters
  • Transformers: Energy transfer between circuits
  • Electric Motors: Creating rotating magnetic fields
  • RF Circuits: Tuning and impedance matching

Physics Equations

Inductive Reactance:
XL=2πfLX_L = 2\pi f L
Voltage across Inductor:
V=XLI=2πfLIV = X_L I = 2\pi f L I
Stored Energy:
E=12LI2E = \frac{1}{2} L I^2
Time Constant:
τ=LR\tau = \frac{L}{R}
Impedance:
Z=R2+XL2Z = \sqrt{R^2 + X_L^2}

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Identify Known Values

List the given values from the problem:

Equation:

\text{Given: } L = ${L} \text{ H}, f = ${f} \text{ Hz}, I = ${I} \text{ A}

Calculation:

L=0.1 Hf=60 HzI=1 AL = 0.1 \text{ H} \\ f = 60 \text{ Hz} \\ I = 1 \text{ A}

Explanation:

We start by identifying what values we know and what we need to find.

2

Step 2: Calculate Inductive Reactance

Use the inductive reactance formula:

Equation:

XL=2πfLX_L = 2\pi f L

Calculation:

XL=2π×60×0.1=37.70 ΩX_L = 2\pi \times 60 \times 0.1 = 37.70 \text{ }\Omega

Explanation:

Inductive reactance is calculated using the frequency and inductance.

3

Step 3: Calculate Voltage across Inductor

Use Ohm's Law for reactance:

Equation:

V=XLIV = X_L I

Calculation:

V=37.70×1=37.70 VV = 37.70 \times 1 = 37.70 \text{ V}

Explanation:

The voltage across an inductor is the product of reactance and current.

4

Step 4: Calculate Stored Energy

Use the energy storage formula:

Equation:

E=12LI2E = \frac{1}{2} L I^2

Calculation:

E=12×0.1×12=0.0500 JE = \frac{1}{2} \times 0.1 \times 1^2 = 0.0500 \text{ J}

Explanation:

The energy stored in an inductor is proportional to the square of the current.

Frequently Asked Questions (FAQ)

What is inductance?

Inductance is a property of electrical circuits that opposes changes in current. It is measured in henries (H) and represents the ability of a component to store energy in a magnetic field.

How do I calculate inductive reactance?

Inductive reactance is calculated using Xₗ = 2πfL, where f is the frequency and L is the inductance. It increases with both frequency and inductance.

What is the relationship between voltage and current in an inductor?

In an AC circuit, the voltage across an inductor leads the current by 90 degrees. The voltage is given by V = XₗI = 2πfLI.

How does frequency affect inductive reactance?

Inductive reactance is directly proportional to frequency. Doubling the frequency doubles the reactance, making inductors more effective at blocking high-frequency signals.

What is the energy stored in an inductor?

The energy stored in an inductor is given by E = ½LI², where L is the inductance and I is the current. This energy is stored in the magnetic field.

Why do inductors oppose current changes?

When current changes, it creates a changing magnetic field, which induces a voltage that opposes the change in current. This is known as Lenz's Law.

Practice MCQs

  1. If the frequency is doubled, the inductive reactance becomes:
  2. What is the inductive reactance of a 0.1H inductor at 60Hz?
  3. The voltage across an inductor in an AC circuit:
  4. The energy stored in a 1H inductor with 2A current is:
  5. Which of the following is NOT a unit of inductance?