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EECS 70A Spring 2020 Assignment #1 c Hamidreza Aghasi Due Date: Tuesday, April 14, 2020

The textbook problem numbers are based on 7th edition. Good luck!

Contents Problem 1 (40 points): Electron Movement and Current Generation

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Problem 1.8 from the textbook (20 points)

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Problem 1.19 from the textbook (20 points)

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Problem 1.20 from the textbook (20 points)

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Problem 1 (40 points): Electron Movement and Current Generation

Figure 1: Electrons moving inside a wire In this question we look at the classical mechanics explanation of current generation inside wires. For those of you who are interested to know about the quantum mechanical explanation of current, I recommend this course of Professor Debdeep Jena at Cornell University which also has online lecture videos. Quantum Transport Theory Course Website In this question, the green volumes represent the infinitesimal cross-sections of the wires. Inside the wires electrons move at a speed of 3×105 m/s. 1. For dx=1nm (very small), there is 1 electorn inside the green volume of Fig. 1(a). What is the current inside the wire?(5 points) 2. For dx=10nm (which is also small) the total number of electrons inside the green volume of Fig. 1(a) is 8. What is the current inside the wire?(5 points) 3. A student decides to calculate the current this way: the wire is 6 mm, and the current should be related to the movement of charge across the wire (green volume moving from one end to the other). For electrons with constant speed, v= ∆x ∆t . By assuming ∆x=6mm, he defines the current as dq/∆t. What is the value of the current that he finds? (5 points) 4. Can you explain which one of the previous parts is the most accurate value of the current? What is it that the student is assuming wrong?(10 points) 5. In Fig.1(b), we divide the electrons between two wires and as you can see the density of charges inside the new green volumes is halved (lighter green color!). For example for dx=10nm, 4 electrons exist in each of the light green volumes. What is the current inside each of these parallel wires if the speed of electrons remains the same? What is the net current of the two wires, i.e., Iup + Ibottom.(10 points) 6. In Fig.1(c), we replace one of the wires with a more expensive wire. Electrons are very smart (at least they act very smart) and prefer to move inside the better wire. For dx=10nm, 6 electrons exist in the top green volume and 2 electrons at the bottom green volume. What is the current inside each wire? Is the net current of the two wires (Iup + Ibottom) the same as before? (5 points)

Problem 1.8 from the textbook (20 points) The current flowing past a point in a device is shown in Fig. 2. Calculate the total charge through the point.1

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Problem 1.8 from the textbook (20 points)

Figure 2: Schematic of Q 1.8

Problem 1.19 from the textbook (20 points) Find i and the power absorbed by each element in the network of Fig 3.

Figure 3: Schematic of Q 1.19

Problem 1.20 from the textbook (20 points) Find V0 and the power absorbed by each element in the network of Fig 4

Figure 4: Schematic of Q 1.20

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