Faradays law: magnetic coil question

[Niz1]

Homework Statement

(The information is for several questions and i have posted one of them)

Two coils magnetically coupled, Voltage of 240v, 50Hz applied to coil 1, current of 2A flows, second coil connected only to a high impedance rms voltmeter reading 100v

find: The peak total flux linkage with coil 1

Homework Equations

e = d{lamdar}/dt

The Attempt at a Solution

ok re-arranging the equation to find {lamdar} which is the flux linkage in coil 1

{lamdar}=et

e = 240 (as given)
t = 1/f (and as radial 2 x pi x f) so t = 1/(2 x pi x f)
t = 2.18... x10-3

so {lamdar}= 0.7639 Wb-turns

but the answer given say should be 1.079Wb-turns

please help will be very gratefull have been at this for hours now.

 

[Jhero]

Dear Forum Member,

Thank you for your post. From your calculations, it seems that you have correctly found the flux linkage in coil 1. However, the given answer of 1.079 Wb-turns may be taking into account the coupling coefficient between the two coils. The coupling coefficient, denoted by k, is a measure of how well the magnetic field from one coil "couples" with the other coil. It is a value between 0 and 1, where 0 means no coupling and 1 means perfect coupling.

To find the peak total flux linkage, we can use the formula:

{lamdar} = k x {lamdar}1

where {lamdar}1 is the flux linkage in coil 1 and k is the coupling coefficient.

In this case, since the two coils are magnetically coupled, we can assume that k = 1. Therefore, the peak total flux linkage would be:

{lamdar} = 1 x 0.7639 Wb-turns = 0.7639 Wb-turns.

I hope this helps and clarifies the discrepancy between your answer and the given answer. If you have any further questions, please let me know.

Scientist