ECE-101

ECE-101
Homework1
All questions are equal points (4 points each)

1. Write out the formula that describes the relationship between resistance and resistivity. Explain the difference between resistance and resistivity.
2. Consider a copper wire and an aluminum wire side by side at the same temperature with exactly the same size/length and geometrical features. Which wire will have a smaller resistance?
3. Calculate the resistance of an aluminum conductor (square cross-sectional area) with a given resistivity=2.6548×10-8 ohm m that is 0.5 meters in length and a width of 1mm.
4. The longer the conductor, the greater or lower will be the resistance?
5. Calculate the length of a copper conductor (round cross-sectional area) with a given resistivity=1.678×10-8 ohm m (resistivity of copper at 20 degrees celsius) and a radius of 2.5 mm with a resistance of 2 Ohms.
6. Calculate the radius of a circular copper conductor (at 20 degrees celsius) that is 25 m long with a resistance given to be 12 Ohms
7. Using circuitlab, draw a schematic of an electrical circuit with a battery and 4 resistors (R1 R2 R3 and R4) that are connected in series to each other and also in series to the battery in a closed loop. Keep in mind that circuitlab has an icon for a battery under the section “unsorted elements”. Make sure to set the internal resistance of the battery to 0 Ohms by changing the R_ESR value from 2 Ohms to 0 Ohms. The battery supplies 25 V and R1 has a resistance of 2k O, R2 has a resistance of 2kO, R3 has a resistance of 4k O and R4 has a resistance of 8 kO

Questions 8-13 are all related to the circuit you drew in question 7
8. Calculate the current IT (in terms of milliAmperes-mA) flowing through the circuit. Show all your work/calculations!
9. Simulate the circuit in circuitlab and display the value of the current flowing through the circuit by appropriately connecting an ammeter to display the current. Make sure you connect the ground appropriately before the simulation.
10. Connect a voltmeter in parallel to the two terminals of R3 and show the voltage displayed on the voltmeter.
11. Now Calculate the voltage distributed across R3 and compare your result with that displayed by the voltmeter in the previous question. Did the simulation and calculation give you the same result?
12. Calculate the voltage drop across resistors R1, R2 and R4.
13. Calculate the power consumed by each resistor R1, R2, R3 and R4.
14. Calculate the combined/total/equivalent resistance RT of 4 resistors connected in parallel to each other with resistances of 50 O, 400 O , 500 O and 800 O respectively.
15. Are the two circuits below functionally equivalent to each other?
16. Calculate the combined/total/equivalent resistance RT of the circuit below.
17. How many KVL loops can you identify in the circuit above? Write out all of the KVL expressions corresponding to the number of loops you found. ie. for N loops you need to write out N KVL expressions. Make sure you designate V1 as the voltage across R1, V2 as the voltage across R2…. and V7 as the voltage across R7 respectively.
18. Determine the voltage V1, V2, V3, V4, and V5 across each resistor in a series circuit with 5 resistors connected in series to a battery supplying 20 V if R1=2R2 and R3=R4=R5=6R1

19. For the circuit below, calculate the voltage V1 and V6. Show your work!
20. For the circuit below, calculate the current displayed on ammeter AM1 corresponding to the current flowing through resistors R5 and R6. Show your work!
21. For the circuit below, calculate the power consumed by resistor R5.

22. Explain how the circuit below will behave. Hint: Consider the resistance of the rightmost branch in the circuit

23. Given the 4 resistors in parallel as shown in the circuit below, derive the expression for RT if 1/RT=(1/R1)+)1/R2)+(1/R3)+(1/R4)

RT=____________________________________
24. Determine the value of the resistance of an SMT resistor if the following value is imprinted on it: 2R6
25. Determine the value of the resistance of an SMT resistor if the following value is imprinted on it: 3456

Tip: When using circuitlab, save your circuit schematics using “File” and then “Save As”. You can then use the Print/Export PDF option under “File” in build mode to export your schematic. Once you export to pdf, you can print the file and submit as part of the hw submission or press the Ctrl+PrtScn buttons to capture a screen shot and embed the screen shot (cropped) into your typed up hw submission (if you prefer to type up your HW).

Good Luck!