- #1

- 147

- 5

## Homework Statement

Two coils of wire that have same shape and dimensions are thickly rolled up so that the coincide, they only differ in number of coils (windings) N1 for the firs one and N2 for the second one (N1<N2). When there's constant current in the first one and there's no current in the second one then fluxes through those two coils are the same. Determine the expression for coupling coefficient of these two coils.

## Homework Equations

##k=\frac{ |L_{12}| }{\sqrt{L_1 L_2}}##

## The Attempt at a Solution

[/B]

In case when there's no current in the second coil and there is constant current in the second coil then there's no magnetic induction vector coming from the second coil so only flux second coil has is flux coming from the first coil ##Ф_{12}=N_2L_{12}I_{1}##, while flux in the first coil is the flux coming from it's own magnetic induction vector (it's own current) and it's value is ##Ф_1=N_1L_1I_1##.

Since these two are equal it means that ##N_2L_{12}I_{1}=N_1L_1I_1 \Rightarrow N_2L_{12}=N_1L_1 \Rightarrow L_{12}=\frac{N_1L_1}{N_2}##

But i don't know how to find ##k=\frac{|L_{12}|}{\sqrt{L_1 L_2}}## because this tells me nothing about ##L_2##. Anyone knows what can i do here?