Resistance of long wires: A pair of Helmholtz coils is to be constructed by wind

Question

Resistance of long wires: A pair of Helmholtz coils is to be constructed by winding 14-gauge copper wire into coils of radius 0.75 m. Each coil will have 120 turns (there could perhaps be some variation in the length of wire in each coil due to how it is wrapped). A constant current of 10 A needs to flow through both coils to produce the desired magnetic field. Look up the resistance of this wire type and size and determine the resistance of each coil. Should the coils be connected to their driving power supply in series or parallel? (we want current to be constant to produce a stable B-field) What is the resistive load seen by the power supply? What minimum voltage compliance is required of the power supply to drive the constant 10 A?

Explanation / Answer

- length of wire used in 1 turn = 2 pi R

L = 2 x pi x 0.75 = 4.71 m

cross sectional area of wire used = pi (1.83 x 10^-3 / 2)

A = 2.63 x 10^-6 m^2

{ 14 gauge means 1.83 mm }

R = rho L / A

= (1.68 x 10^-8) ( 4.71) / (2.63 x 10^-6)

= 0.03 ohm ........Ans

- current is constantthrough each coil that means they are connected in series.

- R = r + r + ----120 time = 120 x0.03 = 3.61 ohm

- V = I R

V = 10 x 3.61 = 36.1 Volt

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