E17M.1 Suppose that we have a fixed length of wire that we would like to wind ar

Question

E17M.1 Suppose that we have a fixed length of wire that we would like to wind around a cylindrical form in a single layer of closely spaced turns to make it more compact, and we would like to minimize the coil’s inductance. Assume that all of the available forms have a small enough radius that the coil’s length will be much larger than its radius.

A) Should we choose the form with the largest radius, the smallest radius, or does it matter? Explain.

B)If we wind the coil in two layers (and use glue to hold the wound wire in place), explain how we might wind the coil so that it has almost zero inductance.

Explanation / Answer

Inductance of solenoid is given by

L = uo N^2 pi r^2 l

here N is no. of turns per unit length

r is radius

l is solenoid

let d be the diameter of the wire, and L be length of the wire

then No. of tunrs = L/2piR

length of solenoid = N * diamter

l = (L/2pir) * d

No. of turns per unit n = N/l

n = (L/2pir)/(Ld/2pir) = 1/d

Inductance of solenoid = uo (1/d)^2 * pi r^2 (Ld/2pir)

Inductance = uo L r/2d

A: to have smaller inductance , radius should be large

B: to get zero inductance, half of coil ihas to wounded opposite to the remaining half coaxially

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