# Mutual inductance in a spark plug

1. Feb 20, 2012

### frogjg2003

1. The problem statement, all variables and given/known data

The ignition coil supplies V=20kV to the spark plugs.
The maximum current in primary coil Imax=4.0A.
The current is interrupted 100 times/sec by the distributor points.

Estimate the mutual inductance M of the primary and secondary coils.
Hint: I have to make a reasonable model of the current I(t).

2. Relevant equations

$\Phi$1=MI2
$\Phi$2=MI1
$\Phi$ is the magnetic flux through the coil

I don't think it's necessary, but Neumann's equation might be useful.

3. The attempt at a solution

I can't visualize what this is supposed to look like. I'm assuming the two coils are coaxial. Are they interwoven? Is one inside of the other? Do they have the same coil density or number of turns?

The other problem I'm having is that I can't decide what a good model function to use for the current.
My best guess would be either a sinusoidal function, or a periodic exponential function.

2. Feb 21, 2012

### frogjg2003

I think I figured it out.
There was a very short part in the chapter that talked about spark plugs. Right before, it gave the equation:
EMF=-M dI/dt
Assuming that the current has the form:
$I(t)=I_{max}ft, 0≤t≤\frac{1}{f}$
$I(t+\frac{1}{f})=I(t)$

Then, ignoring sign, the mutual inductance becomes
$M=\frac{V}{I_{max}f}=0.5H$