Inductance Formula

What is Inductance Formula?

the formula for inductance in an electrical coil is essential for comprehending how electromagnetic circuits operate. This formula is represented as:

L = NΦ / I

• L is the inductance.
• N represents the number of turns in the coil.
• Φ (phi) is the magnetic flux through one turn of the coil.
• I is the current flowing through the coil.

To derive this formula, start by considering Faraday’s Law of Electromagnetic Induction, which states that the induced EMF in a coil is proportional to the rate of change of magnetic flux through the coil. If the flux changes as a result of a change in current, the proportionality constant between the induced EMF (ε) and the rate of change of current is the inductance 𝐿. Thus, we express this relationship as:

ε = -L (dI/dt)

Here, the negative sign indicates that the induced EMF acts to oppose the change in current, according to Lenz’s Law. If you integrate this expression under the assumption of constant inductance, you can correlate the total flux (NΦ) to the current and number of turns, leading to the formula stated.

The concept of inductance was discovered by Joseph Henry in the 1830s, around the same time Michael Faraday was working on electromagnetic induction. Henry’s work was instrumental in advancing the understanding of electromagnetic fields and their practical applications, like in the design of electric motors and generators.

Application of Inductance Formula

1. Designing Transformers: Engineers use the inductance formula to design transformers that efficiently transfer electrical energy between circuits through electromagnetic induction.
2. Building Inductors: The formula helps in creating inductors which regulate current and filter noise in electrical systems.
3. Developing Electrical Motors and Generators: It allows for the design of motors and generators by predicting how magnetic fields interact with electrical currents.
4. Creating Tuned Circuits: Technicians apply the formula to design tuned circuits in radios and TVs to select desired frequencies.
5. Improving Energy Storage Systems: It assists in developing systems like magnetic energy storage, optimizing how energy is stored and retrieved.
6. Suppressing Surge Currents: The formula is instrumental in designing circuits that prevent surge currents, protecting sensitive electronic components.

Examples Problems on Inductance Formula

Problem 1: Finding the Inductance of a Solenoid

Problem Statement: A solenoid has 200 turns and a magnetic flux of 2×10⁻³ webers per turn when a current of 5 amperes flows through it. Calculate the inductance of the solenoid.

Solution: Use the formula

𝐿 = 𝑁Φ / 𝐼​.

Substitute the given values: 𝐿=200×2×10⁻³ / 5=0.08 H

The inductance of the solenoid is 0.08 Henry.

Problem 2: Calculating Inductance with Changed Current

Problem Statement: If the current in the above solenoid changes to 10 amperes, what is the new inductance, assuming magnetic flux per turn remains the same?

Solution: Substitute the new current into the formula:

𝐿=200×2×10⁻³ / 10=0.04 H The new inductance is 0.04 Henry.

Problem 3: Adjusting Turns to Achieve Desired Inductance

Problem Statement: You need to achieve an inductance of 0.5 Henrys in a solenoid with a magnetic flux of 5×10⁻³ webers per turn and a current of 2 amperes. How many turns must the solenoid have?

Solution: Rearrange the formula to solve for N:

𝑁=𝐿×𝐼 / Φ​

𝑁=0.5×2 / 5×10⁻³ =200 turns

The solenoid must have 200 turns.

FAQs

What is Inductance and SI Unit?

Inductance measures an electrical component’s ability to store energy magnetically; its SI unit is the Henry (H).

What is Inductance and Inductor?

Inductance is an electrical property that quantifies a circuit’s capacity to induce voltage from a change in current. An inductor is a device that utilizes this property.

Is inductance AC or DC?

Inductance affects both AC and DC circuits, but its properties become particularly significant in altering current flow in AC circuits due to frequency-dependent behavior.