Problem 74-8
Source: Problem elaborated by the author of the site.
An enameled wire of 17 AWG gauge is used, which has a diameter of 1.15 mm and can be
conduct, at most, a current of 3.2 A, for the construction of a coil formed by
400 turns in a cylindrical shape 10 cm in diameter. Determine.
a) the maximum voltage that can be applied to the coil.
b) in this case, what is the value of the magnetic induction field.
Note: By table 02-01 we have that the resistivity of copper is worth ρ = 1.69 x 10-8 ohm.metro.
Solution of the Problem 74-8
Initially, we will determine the length of the wire used in making the bobbin. We know that the length of a loop is
given by l = π D, where D is the diameter of the wire. Then, multiplying by the number of turns,
we find the total length of the wire, or
On the other hand, the area of the straight section of the wire is
A = π D2 / 4 = 1.04 x 10-6 m2.
Then, using the eq. 02-01, reproduced below, we can calculate the electrical resistance of the coil.
Ssubstituting the numerical values and performing the calculation, we obtain:
As we know that the wire supports a maximum electrical current of 3.2 A, so the maximum voltage
that it is possible to apply on the coil is
In this item we are going to calculate the magnetic induction field of the solenoid (coil) using
eq. 74-23 reproduced below:
Where, in eq. 74-23, Ls represents the length of the solenoid. How do we know the diameter
of the wire and the number of turns, we can calculate the length of the solenoid, or
Then, substituting the numerical values into eq. 74-23, we have
Carrying out the calculation, we obtain:
