Ohm s Law. What You ll Need A computer that can run JAVA applets Calculator Paper & Pencil for calculations.

Transcription

1 Ohm s Law What You ll Need A computer that can run JAVA applets Calculator Paper & Pencil for calculations. Ohm s Law, shown below, is a very important in the analysis of electrical phenomena and is especially important in electronics. VV = IIII If there is an electrical potential difference between two points on a conducting object (e.g. points A & B below), then current will flow between those points, and Ohm s Law relates the potential difference VV to the current II. The constant of proportionality is RR, the resistance between the two points. For example, the electronic circuit shown below is designed to make a siren sound. The zigzag lines are symbols for resistors. Their resistances are indicated. Bananas are poor electrical conductors, which means that the resistance between the two points is very high (between these two points perhaps 20 to 40 MMΩ). We will be working with resistors, which are electronic components with carefully preset resistances (picture below). Electronic circuits can contain many resistors with a wide range of resistances. We ll build some simple circuits (simpler than the one above) using an online circuit simulation tool, which is accessible at this link. To start up the tool, go to the link and click on the play icon (like the one shown here). You might have to click on DOWNLOAD, and then Open. If you cannot start the simulation, your computer might not have a recent version of JAVA. Procedure 1. The available components appear at the right edge of the blue circuit field. Grab a battery and put it into the field.

2 2. Checking the voltmeter box will make a voltmeter appear in the field. You can move it around and also move the probes. Move the probes to the two ends of the battery and read the voltage. VV = VV 3. Change from lifelike to schematic, and also check show values. Then right click on the battery and choose change voltage. Change the voltage to 12 VV and note that the voltmeter will now read the new voltage. 4. Check the Ammeter box, then drag the ammeter into the circuit field. 5. Now construct the circuit shown below. The next figure shows one possible construction of it. 6. Using Ohm s Law and the voltage and resistance, compute the theoretical current. Show the calculation here. 7. Does your calculation agree with the measured value? 8. Right click on the resistor and change the resistance to 50 Ω. This should alter the current in the circuit. 9. Compute the new current using the voltage and new resistance. Show the 10. Does your answer agree with the Resistors in Series and Parallel When multiple resistors are connected in series, as in the figure below, the total resistance of the circuit is the sum of the individual resistances, RR tttttt = RR 1 + RR Put a second resistor in your circuit so that it s wired in series with the first, as

3 in the diagram above. Set the two resistances to RR 1 = 10 Ω & RR 2 = 20 Ω. 12. Given that the new resistance of the circuit is the sum of the resistances of the two resistors, use Ohm s Law to compute the new current. Show your 18. Now measure the voltage across resistor 2 by moving the probes of the voltmeter to its ends. VV 2mmmmmmmm = VV 19. Does your calculated answer agree with your measured answer? 20. Calculate VV 1 using Ohm s Law, the current, and RR 1. Show your work below. 13. Does your calculation agree with the 14. Change the voltage of the battery to 100 VV and compute the new current. 21. How are VV 1 & VV 2 related to the total voltage of the circuit (the voltage of the battery)? Write an equation to express this relationship. 15. Is your answer consistent with the 16. Record the total resistance and the present current. RR tttttt = Ω II = AA 17. Ohm s Law holds for the resistor series, but it also holds for each of the resistors individually: VV 1 = II 1 RR 1 & VV 2 = II 2 RR 2, where VV 1 is the voltage across just resistor 1 and VV 2 is the voltage across just resistor 2. Given RR 2 and the current you just recorded (which is II 2 ), use Ohm s Law to find VV 2. Show your 22. Now wire the resistors in parallel, as in the figure below. You ll have to reduce the voltage of the battery to 50 VV or it will be overloaded (it s just a simulation of course, but they re trying for realism). 23. Record the voltage and current. VV = VV II = AA 24. The two resistors act as one, and the combination of the two should obey Ohm s Law as though it were a single

4 resistor. Given the voltage and current you just measured, use Ohm s Law to find the equivalent resistance of the two resistors in parallel. Show your same manner as two in parallel. The equivalent resistance is given by: 1 RR eeee = 1 RR RR RR You ve seen in lecture that the theoretical equivalent resistance of two resistors in parallel is: 1 = RR eeee RR 1 RR 2 Use this equation to compute the theoretical RR eeee. RR eeee = Ω 26. Does this theoretical calculation of RR eeee agree with the one you determined using voltage and current? 27. You can see in the simulation that some of the current goes through resistor 1 and some through resistor 2. You can measure each of these individually. Click the Non-Contact Ammeter box. This produces an ammeter that, unlike the one you re already using, doesn t need to be inserted into the circuit. You can hover the crosshairs over a wire to measure the current. Use it to measure the two currents. II 1 = AA II 2 = AA 28. Because the total current is being divided between the two resistors, the sum of their currents should equal the total current. Is this the case? 29. Let s do a few more circuits. Make the circuit below. It has 3 resistors in parallel, with resistances 10 Ω, 20 Ω & 30 Ω. Their resistances combine in the 30. Compute the equivalent resistance. 31. Now use Ohm s Law and the voltage and current to compute the resistance of the circuit. RR eeee = Ω 32. Do your two calculations of RR eeee agree? 33. Now make the next circuit. Their resistances should be 10 Ω, 20 Ω, 30 Ω & 40 Ω, and the battery should have 100VV. 34. Can you figure out how to compute the equivalent resistance of all the resistors together? (Hint: It must be done in steps) Show your work below.

5 41. Given this relationship, calculate VV Now compute the resistance using Ohm s Law, the voltage, and the measured current. 42. Given that this is the voltage across resistors 2 & 3, use Ohm s Law and RR 2 and RR 3 to calculate the currents through them. 36. Do your two calculations of RR eeee agree? 37. All the current through the ammeter also goes through resistor 4. Given this and RR 4, calculate VV Likewise, calculate VV Does the entire current go through resistor 2? 40. Does the entire current go through resistor 3? You can determine the currents through these two resistors if you can determine the voltage across them (which is the same). To do this, note that the voltage of the battery is related to the other voltages in the following way: VV = VV 1 + VV 2 + VV 4