ENGR 40M Problem Set 1

Transcription

1 Name: Lab section/ta: ENGR 40M Problem Set 1 Due 7pm April 13, 2018 Homework should be submitted on Gradescope, at The entry code to enroll in the course is available at Problem 1: Reference directions (8 points) Write down the labeled voltages and currents. Pay attention to the reference directions drawn on the components. Don t forget to write the unit. i 2 2 V v 1 v 1 = 4 A i 2 = i 3 6 A i 3 = 3 V v 4 v 4 = i 5 1 A i 5 = 2 V v 6 v 6 = i 8 v 7 = v 7 10 ma 1 V i 8 =

2 Problem 2: Kirchoff s laws (6 points) Consider the following circuit: i T v A i 2 v B 5 V i 1 v O i 3 v C v D i 4 You are given that i 1 = 2 ma, i 4 = 4 ma, v A = 2 V, and v B = 1 V. (a) Find the currents i 2 and i 3, as well as i T. (b) Find v C and v D. (c) Find the power in each device, including the 5 V power source (use passive convention). 2

3 Problem 3: Power dissipation (4 points) Resistors come in lots of different shapes and sizes. Most resistors that we ll use in this course are through-hole resistors, pictured below left. In miniature designs, though, much smaller resistors are used. The chip resistors pictured below right are known as sized resistors. They measure about 0.5 mm 0.5 mm mm pretty small and tough to solder! through-hole resistor 0202 resistor The other catch with such small resistors is that they can t handle very much power. We call the maximum power that a resistor can handle without getting damaged the power rating of the resistor. The pictured resistors are rated at just 40 mw at room temperature. It is the responsibility of the circuit designer to ensure that the circuit doesn t cause them to dissipate that much power (or to use a different-sized resistor). (a) Determine the maximum DC voltage that can be applied across an 0202-sized resistor of resistance 10 kω, without exceeding the power rating of the resistor (that is, before the resistor dissipates more power than it can without getting damaged). Another limit on these resistors is called the breakdown voltage or flashover voltage. Above the voltage, the current can take a shortcut around the resistor, for example, by arcing through air. The resistor pictured above has a breakdown voltage of 50 V. (b) What is the range of resistance values for which an 0202 resistor will experience breakdown, before it burns up due to exceeding the 40 mw power rating? 3

4 Problem 4: (8 points) Series and parallel (a) On the circuit diagrams below, circle the pairs of resistors which are in series. For the purposes of this problem, don t include larger combinations that will be in series after some simplification. Hint: There are a total of 3 pairs. Some circuits might not have any. (b) On the diagrams below, circle the pairs of resistors which are in parallel. Again, don t circle larger combinations. Hint: There are a total of 3 pairs. Some circuits might not have any. A B C D 4

5 Problem 5: More circuits (9 points) Consider the following circuit. Pay attention to the reference directions given on the circuit diagram! R 2 = 10 kω R 1 = 40 kω v 1 v 2 i 1 v 3 R 3 = 20 kω R4 = 20 kω i 3 (a) Find the voltages v 1, v 2 and v 3. (b) Find the currents i 1 and i 3. (c) Find the power dissipated by each of the three resistors. (d) Find the power supplied by the voltage source (i.e., the negative of the power dissipated by the voltage source). 5

6 Problem 6: Your non-ideal multimeter (15 points) We ve seen in class that the ideal voltmeter looks like an open circuit, and that the ideal ammeter looks like a short circuit, so as not to affect the circuit it s measuring. However, in real life the world in which engineers operate voltmeters and ammeters aren t ideal. Voltmeters take a small current, and ammeters a small voltage, in order to operate. In this problem, we ll study the non-ideal ammeter. One way to model an ammeter that takes a small voltage is to model it as an ideal ammeter in series with a resistor of resistance R m (the ammeter symbol represents the ideal ammeter): A R m We ll study how this ammeter affects our measurement of the current in the following circuit: V = 4 V i R = 50 Ω (a) Draw the same circuit, but with an ideal ammeter inserted to measure the current i. (b) Find the current i, that is, the current an ideal ammeter would read. 6

7 Now we ll use a non-ideal ammeter. Assume that the ammeter has non-ideal resistance R m = 1.2 Ω. (c) Draw the model for the non-ideal ammeter inside the blue box below, to complete the circuit diagram. V = 4 V i R = 50 Ω (d) What current will this non-ideal meter measure? non-ideal ammeter Your classmate missed the memo about not connecting ammeters in parallel, and instead connected the non-ideal ammeter to the circuit in the way that voltmeters are supposed to be connected. (You should never do this, by the way.) (e) Draw the model for the non-ideal ammeter inside the blue box above, to complete the circuit diagram. V = 4 V R = 50 Ω non-ideal ammeter (f) Assume the ammeter somehow, magically, doesn t get fried as a result. What current will your classmate measure? 7

8 Problem 7: (2 points) Reflection (a) How long did it take you to complete this assignment? (b) Which problem was the most difficult, and why? 8