## Thursday, August 13, 2009

### Inductance - 7 out of 10 and some lessons learned

Countdown Timer: 7 weeks 5 days to go

I tried the 10 questions on inductance in John Bowyer's Towards the Radio Amateurs' Examination last night. I got 7 out of 10 right, and fell into a couple of traps, which I will try to highlight here in the hope you don't do the same thing.

But first, I must quote some of the introductory material on inductors to help familiarise you with some of the detail.

A circuit has a self-inductance of 1H if a rate of change of current of 1A/s in the inductor induces in it an e.m.f. of 1V.

The mutual inductance between two circuits is 1H if a change of current of 1A/s in one induces an e.m.f. of 1V in the other.

The inductance of a coil is proportional to its:

cross sectional area
the square of the number of turns
and inversely proportional to its wound length.

Assuming no mutual inductance, for inductors both in series and in parallel, the equivalent inductance may be found using similar expressions as with resistors. i.e.:

Series: R1+R2 - L1+L2 Parallel: R1xR2/R1+R2 - L1xL2/L1+L2

All inductors possess resistance. When an inductor is connected across a d.c. supply, the current takes a finite time to reach its final value of V/R. The time constant is an indication of the rise of this current.

Here are two of the three questions I got wrong:

9. Two coils, each of an inductance of 4mH, are connected in series. Their combined inductance
a is 12mH
b is 8mH
c is 2mH
d could be either 2mH, 8mH or 12 mH

Two inductors in series are added, like resistors. So 4 milli henrys plus 4mH = 8mH, right? Yes, but this is the wrong answer, because, as the book explains:

It cannot be assumed that there is no mutual inductance. The combined inductance is not necessarily 8mH.

So d is in fact the correct answer.

10. Two inductors are mutually coupled, and the distance between them gradually increased. Their mutual inductance will
a increase
b remain the same
c decrease
d be immediately zero

I simply didn't know the answer to this question, so I guessed that it would remain the same. The correct answer, however, is c, and this is explained thus:

As the distance between the two inductors is increased, their effect on each other (mutual inductance) will decrease.