Wire length depends on N^2 too.
Hi
Thanks for your comments, at first I thought you are absolutely right. But you made me think a bit.
Are you sure about that? You know I am pretty sure that inductance increases by a power of two when we increase N (number of turns).
But the matter is that the wire length also increases by a power of 2 when increasing N. So I think that in a coil inductance increases almost linearly when increasing the wire length.
For clarification:
1 + 2 + 3 + .... + N = (1 + N)*N/2, So a linear adding up results in a non-linear and a power of 2 increase of the total sum.
So the wire length increases linearly for each turn, when wiring a pancake coil for example the first turn has a wire length of 2pi * r1 and the outer turn will have 2pi* r2 which r1 and r2 are the inner and outer radii respectively. and the total wire length is (2pi.r1 + 2pi.r2)* N/2
where r2 = N * wire_diameter + r1, and N is the number of turns. If we assume that r1 is approximately zero then the total wire length is:
pi * wire_diameter * N^2,
Now I have shown that wire length depends on N^2 too, so we can conclude that inductance depends linearly on wire length which is totally different from the number of turns.
So I hope that I have been able to explain why the time constant remains the same when increasing the wire length.
Kindest Regards,
Elias
Edit: As you mentioned for the other parameters in the formulas for calculating inductance, consider the pancake coil for example, the factor r^2 cancels out by r and d. Remember the Order of change is what counts here, and the order only depends on N^2 both for inductance and wire length for a pancake coil which is quite what we need. the logarithmic parameters do not interfere so much with our results and don't count in.
And as you confirm Einstein, don't let formal education in books be an obstacle to your learning.
Thanks again for making this clear, as It needed to be, it also clarified many things about coils to me too. But nothing can replace true experimentation.
Originally posted by nilrehob
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Thanks for your comments, at first I thought you are absolutely right. But you made me think a bit.
Are you sure about that? You know I am pretty sure that inductance increases by a power of two when we increase N (number of turns).
But the matter is that the wire length also increases by a power of 2 when increasing N. So I think that in a coil inductance increases almost linearly when increasing the wire length.
For clarification:
1 + 2 + 3 + .... + N = (1 + N)*N/2, So a linear adding up results in a non-linear and a power of 2 increase of the total sum.
So the wire length increases linearly for each turn, when wiring a pancake coil for example the first turn has a wire length of 2pi * r1 and the outer turn will have 2pi* r2 which r1 and r2 are the inner and outer radii respectively. and the total wire length is (2pi.r1 + 2pi.r2)* N/2
where r2 = N * wire_diameter + r1, and N is the number of turns. If we assume that r1 is approximately zero then the total wire length is:
pi * wire_diameter * N^2,
Now I have shown that wire length depends on N^2 too, so we can conclude that inductance depends linearly on wire length which is totally different from the number of turns.
So I hope that I have been able to explain why the time constant remains the same when increasing the wire length.
Kindest Regards,
Elias
Edit: As you mentioned for the other parameters in the formulas for calculating inductance, consider the pancake coil for example, the factor r^2 cancels out by r and d. Remember the Order of change is what counts here, and the order only depends on N^2 both for inductance and wire length for a pancake coil which is quite what we need. the logarithmic parameters do not interfere so much with our results and don't count in.
And as you confirm Einstein, don't let formal education in books be an obstacle to your learning.
Thanks again for making this clear, as It needed to be, it also clarified many things about coils to me too. But nothing can replace true experimentation.
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