What is the maximum B-field in the iron core?

In summary, the conversation discusses a student's attempt to light a 12V lamp with a 2V rms AC supply using a transformer with a ratio of 6:1. The question posed involves finding the maximum B-field in the iron core with given values for Ns, Vs, and the cross-sectional area of the secondary coil. The question is deemed difficult due to the teacher's use of differentiation in solving it.
  • #1
Clari
62
0
A student wishes to light a lamp rated 12V, yet he has only a 2V rms a.c supply with variable frequency. So he attempts to step up the voltage by means of a transformer. Given Ns:Np = 6:1, resistance in the primary circuit is 70 ohm, inductance of primary coil is 0.3H, frequency f is 50Hz

a.) If Ns = 600, Vs = 10V (rms), cross-sectional area of the secondary coil is 2cmx2cm, what is the maximum B-field in the iron core?

i find this question really difficult, because my teacher uses differentiation to solve it...:confused: i wonder if there are simple ways to solve it. Thanks!
 
Physics news on Phys.org
  • #2
[tex]\frac{\Delta (B \cdot A)}{\Delta t} = E \cdot circumference[/tex] .

in 1/200 sec (that is, .005 s), B changes from zero to its maximum.
You might expect that the greatest rate of change in B is 200/s times B_max ;
but in fact, the greatest rate of change in B is (2 pi f) times B_max .
(recall velocity of an oscillator?)
This is why you really need to take derivitives.
 
  • #3


The maximum B-field in the iron core can be calculated using the formula B = μ0μrNI/l, where μ0 is the permeability of free space, μr is the relative permeability of the iron core, N is the number of turns, I is the current, and l is the length of the core.

To solve this problem, we first need to find the current in the primary circuit. Using Ohm's law, we can calculate the current as I = Vs/Rp, where Vs is the supply voltage and Rp is the resistance in the primary circuit. Substituting the given values, we get I = 2V/70ohm = 0.0286A (rms).

Next, we need to find the number of turns in the secondary coil. We are given that Ns:Np = 6:1, so we can calculate Ns as Ns = Np x 6 = 600.

Now, we can use the formula for B-field to calculate the maximum B-field in the iron core. Substituting the given values, we get B = (4π x 10^-7) x (2000) x (600) x (0.0286A) / (0.02m) = 0.0214T

Therefore, the maximum B-field in the iron core is 0.0214T. This value may seem small, but it is enough to produce a significant magnetic field and light the lamp. It is important to note that this calculation assumes ideal conditions and does not take into account any losses in the transformer.
 

1. What is a B-field and why is it important in an iron core?

A B-field, also known as a magnetic field, is a region in space where a magnetic force can be felt. In an iron core, it is important because it is responsible for creating a magnetic field that allows the core to function as an electromagnet.

2. How is the maximum B-field determined in an iron core?

The maximum B-field in an iron core is determined by the material properties of the core, such as its magnetic permeability and saturation point, as well as the amount of current flowing through the core.

3. What is the relationship between the B-field and the amount of current flowing through the iron core?

The B-field in an iron core is directly proportional to the amount of current flowing through it. This means that as the current increases, the B-field also increases.

4. What happens if the B-field in the iron core exceeds its maximum value?

If the B-field in the iron core exceeds its maximum value, the core will become saturated and unable to generate a stronger magnetic field. This can also cause the core to overheat and potentially damage the equipment.

5. Can the maximum B-field in an iron core be increased?

The maximum B-field in an iron core is limited by the material properties of the core. However, it can be increased by using materials with higher magnetic permeability or by increasing the amount of current flowing through the core, up to a certain point before saturation occurs.

Similar threads

  • Electromagnetism
2
Replies
42
Views
721
Replies
8
Views
938
  • Electrical Engineering
Replies
3
Views
1K
  • Electromagnetism
Replies
2
Views
1K
  • Electrical Engineering
Replies
11
Views
2K
  • Electrical Engineering
Replies
5
Views
3K
Replies
1
Views
2K
  • Electromagnetism
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
3K
Back
Top