# Find the inductance and a current of a coil

• awesome2999
In summary, to calculate the inductance of the coil and the current at which the ferrite saturates, use the equations mentioned above and plug in the appropriate values for the variables. The inductance is 0.000139 H and the current is 5.5796 A.
awesome2999
Hi everybody, i have got a question,any help will be much appreciated

A ferrite ring core has a slot cut in it such that the plane of the slot contains the axis of the toroid. It is wound with 26 turns.

i have attached the picture of the this problem.

Relative permeability = 680
Bsat = 0.38T

Ignoring leakage and fringing:

What is the inductance of the coil?

At what current does the ferrite saturate

the equation I'm using is N^2/((lair/MoMr*Aair)+(l iron/MoMr*Airon))

l air is 0.0003m
Aair = Airon= 1.22518E-3 i calculated this one
i'm not sure for liron shoud i use 0.0039*pi and substruct from lair. but still i don't get the right answer.

the right answer should be is L=0.000139 H and I=5.5796 A

for the current still don't get the answer right. I'm using B/MoMr=H and then H=NI/2Pi*r

please.any help will be much appreciated.

#### Attachments

• picture ferrite core.jpg
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thanks a lot. The inductance of the coil can be calculated using the equation: L = (N^2 * μo * μr * A) / l, where N is the number of turns, μo is the permeability of free space, μr is the relative permeability of the core material, A is the cross-sectional area of the core material, and l is the mean length of the winding. In this case, the mean length of the winding is equal to the circumference of the toroid, which is 2πr. The cross-sectional area of the core material is its area times the width of the slot. So, the inductance of the coil can be calculated as: L = (26^2 * 4π * 680 * (πr^2 * w)) / (2πr) where r is the radius of the toroid and w is the width of the slot. The current at which the ferrite saturates can be calculated using the equation: I= (Bsat * μo * μr * A) / (2π * l), where Bsat is the saturation flux density of the core material, μo is the permeability of free space, μr is the relative permeability of the core material, A is the cross-sectional area of the core material, and l is the mean length of the winding. In this case, the mean length of the winding is equal to the circumference of the toroid, which is 2πr. The cross-sectional area of the core material is its area times the width of the slot. So, the current at which the ferrite saturates can be calculated as: I = (0.38 * 4π * 680 * (πr^2 * w)) / (2π * 2πr) where r is the radius of the toroid and w is the width of the slot.

## 1. What is the formula for finding the inductance of a coil?

The formula for finding the inductance of a coil is L = (μ0 * N^2 * A)/l, where μ0 is the permeability of free space, N is the number of turns in the coil, A is the cross-sectional area of the coil, and l is the length of the coil.

## 2. How is the current in a coil related to its inductance?

The current in a coil is directly proportional to its inductance. This means that as the inductance of a coil increases, the current in the coil also increases.

## 3. Can the inductance of a coil be changed?

Yes, the inductance of a coil can be changed by altering its physical characteristics such as the number of turns, cross-sectional area, or length. It can also be changed by introducing a magnetic core material into the coil.

## 4. How is the inductance of a coil measured?

The inductance of a coil is measured using a device called an inductance meter. This tool uses a known frequency and measures the voltage and current in the coil to calculate its inductance.

## 5. Why is it important to know the inductance and current of a coil?

Knowing the inductance and current of a coil is important for understanding its behavior in a circuit. It can also help in designing and optimizing circuits for specific applications. Additionally, it is necessary for calculating other important parameters such as impedance and reactance.

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