Induktivität einer Spule

Summary

In this video, the concept of inductance in a coil, or 'Spule,' is explained in detail. The video covers the relationship between current and induced voltage using formulas related to magnetic fields, flux, and Faraday's Law of Induction. By combining these equations, the inductance value of a coil is derived, showcasing how it determines the behavior of voltage and current. The video also emphasizes the practicality of inductance, explaining how engineers can easily determine a coil's electrical characteristics by looking at its inductance value, measured in Henrys.

Takeaways

• 😀 An electrical engineer refers to a coil as inductance in the context of electricity.
• 😀 The goal is to relate the current flowing through a coil to a voltage, establishing a relationship between voltage and current.
• 😀 The formula for the magnetic field inside a long coil is shown: B = μ₀ * μr * n * I / l, where n is the number of turns, l is the length, and I is the current.
• 😀 The magnetic flux is defined as the magnetic field B multiplied by the area A, and this formula can be used to calculate it.
• 😀 The general law of induction is used to calculate induced voltage, where the induced voltage U_int is equal to -n times the time derivative of magnetic flux.
• 😀 The derivative of the magnetic flux is crucial, and only the current, which depends on time, needs to be differentiated.
• 😀 The induced voltage in the coil can be written in terms of the inductance L, which is a measure of the coil's electrical behavior.
• 😀 The inductance formula combines geometric and material properties of the coil, and it is given by L = n² * A * μ₀ * μr / l.
• 😀 Engineers don’t need to measure every electrical property of a coil manually; they can simply look at the inductance to understand its behavior.
• 😀 The unit for inductance is Henry (H), named after American scientist Joseph Henry.
• 😀 The inductance combines all geometric and material characteristics of the coil into a single value, bridging the gap between current and voltage.
• 😀 The explanation also refers to other educational videos on the channel that provide more in-depth details on the formulas used in the video.

Q & A

What is the primary purpose of the video?

The primary purpose of the video is to explain the concept of inductance in a coil, and how to relate the current flowing through a coil to the voltage across it.

How is the magnetic field inside a long coil described?

The magnetic field inside a long coil is described by the formula B = μ₀ * μr * n * I / l, where B is the magnetic field, μ₀ is the permeability of free space, μr is the relative permeability, n is the number of turns, I is the current, and l is the length of the coil.

What is the relationship between current and voltage in a coil?

The relationship between current and voltage in a coil is described by the induced voltage (U) being proportional to the negative time derivative of the magnetic flux (Φ). This is given by the formula U = - L * dI/dt, where L is the inductance and dI/dt is the rate of change of the current.

What is the formula for magnetic flux?

The formula for magnetic flux is Φ = B * A, where B is the magnetic flux density and A is the area of the coil.

Why do we only take the derivative of the current in the inductance formula?

We only take the derivative of the current because the current is the only variable that depends on time. Other factors like the number of turns (n), length (l), and permeability (μ) are constants in this context.

What is inductance and how is it related to a coil?

Inductance (L) is a measure of a coil's ability to oppose changes in current. It is calculated as L = n² * A * μ₀ * μr / l, where n is the number of turns, A is the cross-sectional area, μ₀ is the permeability of free space, μr is the relative permeability, and l is the length of the coil.

What are the units of inductance?

The unit of inductance is the Henry (H), which is named after Joseph Henry, an American scientist.

What does the inductance value of a coil tell you?

The inductance value of a coil tells you how strongly the coil resists changes in current. A higher inductance means the coil will oppose changes in current more strongly.

Why is inductance considered an electrical property of a coil?

Inductance is considered an electrical property of a coil because it describes how the coil reacts to changes in current. It is a combination of the coil's geometric and material properties that determine its behavior in an electrical circuit.

What is the significance of the formula U = - L * dI/dt?

The formula U = - L * dI/dt is significant because it provides a direct relationship between the induced voltage (U) and the rate of change of current (dI/dt) in the coil. It shows that a voltage is induced in the coil when the current through it changes over time.