:For the network below if 7. (t) = 6cos (20t + 30), find a) The amplitude of the output votage = volts b) The phase of the output voltage = □ degrees :For the network below if ¡in(t) = 6cos(20t +30°), find 20 mF fin(t) 0.1 H a) The amplitude of the output votage= b) The phase of the output voltage= +8 50 mF (t) volts degrees

6. Determine the exponential form of the Fourier series of these signals, and draw the amplitude and the phase spectrum. The figure shows for every case a period of length T. ..... (a) (b) (c)

5. Consider a coaxial cable which is an (infinitely) long wire of radius a, with given current flowing uniformly up it (so J(t) = I(t)/лa² goes uniformly through the wire). At the outside edge (r=a), there is an infinitesimally thin insulator, and just outside that, an infinitesimally thin sheath that returns all the current, basically a surface current going down the opposite direction carrying a total -I(t) back down. Figure out the B field everywhere in space (direction and magnitude) in terms of givens, and then find the self-inductance per length of this cable. Assume I(t) changes slowly in time, so we can use our usual quasi-static ideas. There are several ways to proceed. You might start from =LI, but this turns out to be tricky here, since the current is not confined to a single path! It is best to think about the total magnetic energy, W, stored by the magnetic field, and use our usual relation between energy and current: WL I²/2.

Q5: Consider the formula B = 2ol J’ds:e 4 r and give an explanation of the magnetic field unit ?

Q2: A PI controller has K, 2.0, K2.2 s¹, and pi(0)=40%. Calculate the output for an error given by fig. 3 ep (%) -2 Fig. 3 Figure I (seconds)

3 Charged Closed Wire Consider a thin closed wire with the radius R localized at the origin on the xy-plane, which is charged uniformly with the total charge Q. (i) What is the charge density p in this problem? (ii) Calculate the electric field along the z axis? (Hint: First, consider an infinitessimal piece of the charge.)

For the diagram shown, the respective values of n1 and n2 for the following equation are: Po = 50(P/A,i,n1)(P/F,i,n2) are:

1. Imagine a triple-slit "grating", where the distance to the screen is much larger than the distance between the slits. By using phasors, show that the intensity of the interference pattern is given by I = I(1 + 4 cos & + 4 cos² ø). (Hint: Recall the intensity of fringe pattern in Young's two-slit interference experiment.)

the yeild curve at the present time (t=0)

What is the value of (F/A, i, N) if (P/A, i, N) = 6.1343? O a. 3.0672 O b. 5.5209 O c. 6.1343 O d. 1.0000 O e. 36.3400