How is Inductance Calculated? Self and Mutual Inductance Explained with Formulas
Inductance is a fundamental property found in electrical circuits, especially those that involve coils or windings. When an electric current flows through a conductor, such as a coil, it generates a magnetic field around it. If the current changes, the magnetic field also changes, which results in the creation of a voltage (or electromotive force, EMF) either in the same conductor or in a nearby conductor. This phenomenon is known as electromagnetic induction, and the ability of a conductor to produce such an effect is called inductance.
In simple terms, inductance represents how much a conductor resists changes in current by inducing a voltage. This property is especially prominent in coils, which are used extensively in electronic devices and circuits.
Inductance: Definition and Explanation
Inductance is defined as the property of a conductor by which a change in current through it induces an electromotive force, either in the same conductor (self-inductance) or in a neighboring conductor (mutual inductance).
A stationary (steady) current creates a constant magnetic field. However, when the current varies, it causes the magnetic field to change as well, resulting in an induced voltage proportional to how quickly the current changes. This effect is measured by the size of the induced voltage divided by the rate of change of the current.
The SI unit of inductance is the henry (H).
Fundamental Formula of Inductance
Inductance (L) is expressed mathematically as:
More specifically, if the current through a coil changes at a rate of 1 ampere per second, and the induced EMF is 1 volt, the inductance of the coil is 1 henry.
Types of Inductance
There are two main types of inductance:
- Self-Inductance: The induced voltage appears in the same conductor due to a changing current.
- Mutual Inductance: The induced voltage appears in a different, nearby conductor when the current changes in the primary conductor.
For a deeper understanding, explore self and mutual inductance formulas.
Inductance in Action: Step-by-Step Example
Consider a coil of wire. When the current through the coil increases, the magnetic field around the coil also becomes stronger and changes with time.
This changing magnetic field induces a voltage (EMF) in the wire according to Faraday's Law, opposing the change in the original current (Lenz's Law). Thus, the coil resists any alteration in the current.
This property is what makes inductors useful in filtering, timing, and energy storage applications.
Key Inductance Formula Table
| Formula | Description | Units |
|---|---|---|
| L = EMF / (dI/dt) | Inductance based on induced voltage and rate of change of current | Henry (H) |
| L = μ₀N²A / l | Self-inductance of a long solenoid | Henry (H) |
To study further, refer to unit of inductance.
Solving Inductance Problems: A Step-by-Step Approach
1. Define knowns and unknowns: Start by listing what you know (number of turns, area, length, material properties) and identify what needs to be found (such as inductance, induced EMF, or rate of change).
2. Choose the right formula: Select the formula based on the configuration (simple coil, solenoid, or mutual system).
3. Plug in the values: Substitute given values carefully, keeping units consistent.
4. Solve stepwise: Break down the calculation into manageable parts to avoid algebraic or arithmetic errors.
| Step | Action | Purpose |
|---|---|---|
| 1 | Identify current and geometry details | Ensure correct inputs for formula |
| 2 | Apply inductance formula | Establish relation between variables |
| 3 | Calculate stepwise | Reduce mistakes; build understanding |
Practical Relevance and Applications
Inductance is crucial in many real-life applications such as:
- Transformers for voltage conversion
- Filters in communication circuits
- Energy storage in power supplies
- Electrical chokes and relays
Visual Comparison: Inductance vs. Resistance
| Property | Inductance | Resistance |
|---|---|---|
| Physical Meaning | Opposes change in current | Opposes current flow |
| Unit | Henry (H) | Ohm (Ω) |
| Energy Involvement | Stores energy in magnetic field | Dissipates energy as heat |
For more comparisons and practical circuit situations, visit reactance and impedance.
Practice and Further Learning
Practice is vital for mastering Physics concepts. Use the following steps to reinforce your understanding:
- Review solved problems regularly from Vedantu’s inductance page.
- Investigate how inductance is used in daily electronic appliances using Vedantu’s inductor resources.
Next Steps
To build a robust understanding of inductance and its applications, explore these essential topics:
FAQs on Inductance in Physics: Meaning, Formulas & Examples
1. What is inductance in Physics?
Inductance is a property of an electrical conductor (usually a coil) by which a change in current induces an electromotive force (EMF) either in the same circuit (self-inductance) or in a nearby circuit (mutual inductance). Inductance measures the ability to oppose changes in electric current due to the creation of a magnetic field.
2. What is the SI unit of inductance?
The SI unit of inductance is the Henry (H). One Henry is defined as the inductance in a circuit when a change in current of one ampere per second induces an EMF of one volt.
3. What is the inductance formula?
The basic formula for inductance (L) is:
L = NΦ / I
- N = Number of turns
- Φ = Magnetic flux
- I = Current through the coil
4. What is the difference between inductance and resistance?
Inductance and resistance are different electrical properties:
- Inductance (L): Opposes changes in current; SI unit is Henry (H); does not dissipate energy but stores it in a magnetic field.
- Resistance (R): Opposes the flow of current; SI unit is Ohm (Ω); dissipates energy as heat.
5. What is self inductance with example?
Self inductance is the property of a coil or circuit by which a changing current induces an EMF in the same circuit.
Example: When the current through a solenoid is changed rapidly, a back EMF is produced in the solenoid itself that opposes this change, demonstrating self-inductance.
6. How is inductance measured?
Inductance is measured using an instrument called an LCR meter. It determines the coil's inductance by applying an AC voltage and measuring the resulting current and phase angle. The SI unit is Henry (H).
7. What is mutual inductance?
Mutual inductance is the property where a change in current in one coil induces an EMF in a neighboring coil. This is the basic principle behind transformers. The mutual inductance (M) between two coils depends on the number of turns, the area, and the coupling between them.
8. What is the symbol of inductance?
The symbol for inductance is 'L'. The unit is Henry, represented by 'H'.
9. What are the applications of inductance in daily life?
Inductance has many practical applications:
- Transformers for voltage conversion
- Inductors in radio tuning circuits
- Chokes in power supplies
- Electric motors and generators
- Ignition coils in vehicles
10. How do you calculate the self-inductance of a solenoid?
The self-inductance (L) of a solenoid is calculated by:
L = μ0 N2 A / l
- μ0 = Permeability of free space
- N = Number of turns
- A = Cross-sectional area
- l = Length of the solenoid
11. What is the dimensional formula for inductance?
The dimensional formula for inductance is [M L2 T-2 A-2], where M = mass, L = length, T = time, and A = current.
12. What is the relationship between self inductance and mutual inductance?
Mutual inductance (M) between two coils depends on their self-inductances (L1 and L2) and the coupling coefficient (k):
M = k√(L1 L2)
Here, 'k' is the fraction of magnetic flux from one coil linked with the other, with values between 0 (no coupling) and 1 (perfect coupling).
