She has created the circuit above using batteries, resistors, wires, and a light bulb. All batteries have a ∆V of 1 V and all resistors (including the bulb) have a resistance of 1Ω. How much current flows through the bulb? Show how you arrived at your answer

A dipole and a solid sphere of charge +Q are oriented as shown in Figure. The dipole consists of two charges q and - q, held apart by a rod of length s. The center of the dipole and the sphere are at a distance d from the location A. q = 6 nC, s =4 mm, d = 14 cm, and Q = 8 nC. \text { Find the magnitude of the electric field }\left|\overrightarrow{\mathbf{E}}_{\text {dipole }}\right| \text { due to the dipole at the location } \mathbf{A} . (10 points) Draw the direction of the electric field due to the dipole at the location A and write the electric field as a vector Edipole· \text { 5) Find the net electric field vector } \overrightarrow{\mathbf{E}}_{\text {net }} \text { at location } \mathbf{A} \text { due to dipole and the solid sphere. } \text { ) If a proton is placed at location } A, \text { what would be the net electric force vector } \vec{F}_{\text {net }} \text { on the proton? } \text { Find the electric field vector } \overrightarrow{\mathbf{E}}_{\text {Solid sphere }} \text { due to the solid sphere at the location } \mathbf{A} \text {. }

A periscope consists of two 90-45-45º prisms (as shown in Figure) are made of lossless glass with n=1.5. The reflection off the inclined planes are 100% (total reflection per Snell's Law), i.e. |T|= 1. (a) What power(in dB) is the transmitted signal through the bottom prism relative to the input? (b) If the incoming signal has a magnetic field given by: H,(x,f) = 23.77 sin(10"r-kx)mA/m, what is the first reflected E-field? What is k?feld B

Consider the following transfer functions: \text { 1. } \quad G \square_{1}(s)=\frac{s}{s^{2}+10 s+89} 2 \quad G \square_{2}(s)=\frac{s^{2}+25}{s^{3}+4 s^{2}+29 s} \text { 3. } G \square_{3}(s)=\frac{s+10}{s^{2}+15 s+56} For the three transfer functions above, perform the following task in Matlab: For each of the systems above, define the transfer functions in Matlab. Plot the poles and zeros in the complex plane using pzmap. Your answer should be three plots.Comment on the stability of each system. c)Find the unit impulse response of the systems above. Your answer should be three plots. d) Find the unit step response for each of the transfer functions above and plot your input and response on the same plot for each transfer function. Your answer should be three plots e) Generate the Bode Plots for each of the transfer functions above.

5.7 (note: TRL = 0 because it is not given in the problem statement)

2) When light of wavelength 311 nm is shone onto the surface of a particular metal in a vacuum, it is found that a reverse voltage (stopping potential) of 0.6 Vis needed to prevent current flow between the photoemitter and an anode connected externally to it. Calculate the work function of the metal in electron volts(ev) and the most likely energy level (i.e. which orbit) the electrons were ejected from.

1) Triboelectric Series: Find a couple of pairs of materials from the triboelectric series and rub them together. Do they attract each other as advertised? Does the strength of attraction depend on how hard or for how long they are rubbed together? Does the attraction wane with time? Why? Which material is is positive and which one is negative? What practical uses can you imagine for this phenomenon? What dangers? 2) Drying Clothes: Dry some clothes in a tumble dryer or sneak into a laundromat and examine someone else's tumble dried clothes. Find some items that stick together and check their labels for their compositions. What do you see as you pull the clothes apart? What do loose threads do? Why? How is this behavior explained by their composition? What do you hear as you pull them apart? Why? Do wet clothes stick together this way or not? If so,why and if not, why not? This so-called static cling is really tribo electric electrostatic cling.Why do you suppose advertisers call it just static cling? How do anti-static dryer balls and dryer sheets work? Any additional observations you can make are welcome. 3) Scotch Tape: Pull out a couple of stretches of scotch tape from a roll. Is the tape attracted to your skin? How about to glass or metal? Why? Do the two stretches of tape attract or repel each other? Why? Other observations are welcome. 4) One of Your Own: Find your own example of triboelectricity in your home. Experiment with it and describe what you find. Quantitative observations and measurements are welcome welcome.5) Shuffling Shoes: Shuffle your shoes across a carpet and then touch a door knob or some electrically grounded object such that you get a small electrical shock. You might see a small electrical arc. (Better yet, touch the back of someone's ear who's not expecting it,but be prepared to get yelled at.) Explain the shock in terms of the tribolectric series. Did your shoes charge positive or negative? Modern carpets have special chemicals to reduce this effect? How might these antistatic agents work? It's been proposed that this effect can be eliminated by weaving metallic threads through the carpet. Why? 6) Swiffer: How do Swiffer dusters work from the point of view of triboelectricity and induction? 7) Dusty Fan Blades: Find an old fan and look at its blades. Very likely they will have a layer of dust on them. Why should dust settle there, considering that the fan blades turn very fast and, therefore, should shake the dust loose? What holds the dust on the blade sand how did it settle there in the first place? 8) Sparkin' Obtain some wintergreen lifesavers that have some real sugar in them – avoid artificial sweeteners. Go into a dark room, let your eyes adjust for about a minute, then crush the lifesaver quickly. A pair of pliers is ideal, but crunching them in your mouth will also work. If you use your teeth, perhaps do it in a bathroom facing a mirror so you can see into your mouth as the lifesaver is quickly crushed. What do you see? What do you think is going on? In your grandparents' generation, this was a popular pass time: going up to lover'slane and sparkin'.

In the shown figure, C, = C, = Co- 18.6 nF and C, = C = C, = 10.8nF. The applied potential is Vab= 54 v I. What is the equivalent capacitance of the network between points a and b? II. Calculate the charge on the equivalent capacitor ?

Determine the angular accelerations of link BCand the acceleration of C. \omega_{A B}=8^{\text {rad }} /_{s}(\text { CCW }) a_{A B}=10^{\text {rad }} /_{s^{2}}(C W) For the velocity analysis use only the vector polygonmethod. For the acceleration analysis, use only the accelerationdiagram method, graphically and analytically.

The two point charges, q and −q, are 2d apart. We form a z-axis through both charges. Let the two charges be at (0,0,d) and (0,0,—d) in the figure. Let's say that p is any point in space which is very distant (r>>d). (a) Show that the electric potential at point P is \Phi(\overrightarrow{\mathrm{r}})=\frac{1}{4 \pi \epsilon_{0}} \frac{\overrightarrow{\mathrm{p}} \cdot \hat{\mathrm{r}}}{r^{2}} (b) Use equation (11) to prove that the field \overrightarrow{\mathrm{E}}(\overrightarrow{\mathrm{r}})=\frac{1}{4 \pi \epsilon_{0}} \frac{3(\overrightarrow{\mathrm{p}} \cdot \hat{\mathbf{r}}) \hat{\mathbf{r}}-\overrightarrow{\mathrm{p}}}{r^{3}}