Suppose you have a wire of diameter d, length l, and resistivity r , and a volta

Question

Suppose you have a wire of diameter d, length l, and resistivity r , and a voltage source that supplies a fixed potential difference V, Recall, the circumference of a circle is C = 2 pi r where r is the radius. Find the current in the wire when it is connected to the potential applied across the length l. Your answer should be in terms of V, l, d, and rho. Show that if the wire is wound into a single layer coil with coil radius r, coil length L, with adjacent turns touching, the volume of the coil the approximated by the following formula. Note, if the turns are touching the turn density n = l/d Assume coil is an ideal solenoid. Determine the magnetic field inside the coil in terms of the power supply voltage V, wire parameters l, d, rho, and coil radius r. Determine the coil inductance L in terms of the given parameters.

Explanation / Answer

a) R=p*l/S so I=V/R=V*S/p*l. b)number of coil N=L/d. so that total length. 2pi*r*N=2pi*r*L/d so total volume. 2pi*r*L*pi*d^2/4d=pi^2*rLd/2 ---- total length of the coil. N*2pi*r=L*2pi*r/d so that R=p*l/S=p*V/S^2=p*pi^2*rLd/2*(pi*d^2/4)^2=8*p*rL/d^3 so I=V*d^3/8prL. so B=I*N*muy0/L=I*muy0/d=V*d^2*muy0/8prL ----------- magnetix flux. B*pi*r^2=I*muy0*pi*r^2/d so inductance. flux/current. =muy0*pi*r^2/d

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