Assignment:
Problems:
1) Given a metal rod placed along 2 conducting wires connected by a 20 ohm resistor initially forming a 1 square meter area as shown, sketch the voltage reading versus time given the plot of position versus time. Be sure to carefully determine the polarity of the measurement and also show the magnitude of Vin order to get full credit. The B field is 10 Tesla, directed out of the page.
2) Given a known load of ZL = 30 + j70 Ω and a transmission line with Zo = 50 Ω, use a Smith chart to determine a) through c) below. Label your chart where appropriate and plan to turn it in with your test.
a. In polar coordinates, what is Γ at the load.
b. What is the relative impedance zL 0.1 wavelengths toward the generator.
c. If you were to place a series component to make the load at the generator look like a pure 50 Ω, where would you put this component and what would its value be in terms of reactance?
d. If f =1 GHz, what would be the value of the series component be in either farads or henrys
3) A 1-meter conducting rod sits on a pair of conducting wires, and a non-uniform B field, B = B0/(1+ y) az is present coming out of the page. The current through the rod in the direction shown will cause the rod to roll in one direction or the other.
a. Which direction will the rod roll?
b. For I = 20 A and Bo = 10 Tesla, what is the force on the rod?
c. When the rod rolls, the flux through the closed circuit will either increase or decrease. We know nature wants to keep that flux constant and will resist the change. Using the right-hand rule, does the net effect increase or decrease the net current in the loop? (Note that if it increased the current, this would increase the force on the rod and it would continue to accelerate - sounds too good to be true.)