HOMEWORK SET 4 - Due: Tuesday, March. 9
The conductivity of seawater is ~4 S/m. Describe how you would establish radio communication with a submarine. What frequency would you choose? How deep can the submarine be? Consider the fact that at a higher frequency, information can be transmitted at a higher rate.
A ground-fault protection circuit senses an imbalance between the current in the `hot' wire and that in the ground wire. This is done by wrapping both the hot and ground wires (primary, Np = 10) around a high mr (2000) material in the same direction. A design (not actually how it is done) is below. The sense circuit has Ns (100) winds.
At what voltage on the sense circuit (Vs) should the trip activate (open the circuit) if the maximum allowable imbalance is 10 mA on a standard 60 Hz AC circuit?
(a) Calculate the time averaged Poynting vector as a function of penetration distance into a good conductor.
(c) Show that the total energy loss per unit area is 1/2 Rs|Js|2.
A parallel-plane transmission line is diagramed below. You can assume l >> w >> d.
(a) Derive and expression for the magnetic field between the two planes in terms of the current I.
(b) Derive and expression for the electric field between the two planes in terms of the voltage between the plates V.
(c) Derive the inductance per unit length L.
(d) Derive the capacitance per unit length C.
(e) Starting with Maxwell's equations, assuming variation only in t and z, derive the telegraphist's equations (Ramo, 5.2, equations (3) and (4)).
(f) Calculate the required termination for a computer circuit board (e r= 2.5, d = 5 mm, w = 15 mm).