1. PHY 202 (Blum)1 More basic electricity Non-Ideal meters, Kirchhoff’s rules, Power, Power supplies

2. PHY 202 (Blum)2 What makes for ideal voltmeters and ammeters?

3. PHY 202 (Blum)3 Ideal Meters Ideally when a voltmeter is added to a circuit, it should not alter the voltage or current of any of the circuit elements. These circuits should be the same.

4. PHY 202 (Blum)4 Voltmeter Devices in parallel have the same voltage. Voltmeters are placed in parallel with a circuit element, so they will experience the same voltage as the element.

5. PHY 202 (Blum)5 Theoretical calculation 5 V = (1 k  + 3.3 k  ) I 5 V = (4.3 k  ) I I = 1.16279 mA V 3.3 = (3.3 k  ) (1.16279 mA) V 3.3 = 3.837 V Slight discrepancy? Without the voltmeter, the two resistors are in series.

6. PHY 202 (Blum)6 Non-Ideal Voltmeter Ideally the voltmeter should not affect current in resistor. Let us focus on the resistance of the voltmeter.

7. PHY 202 (Blum)7 R V should be large If R v  , then Voltmeters should have large resistances. 1 = 1 + 1 R eq R 3.3 RvRv 1  1 R eq R 3.3 The voltmeter is in parallel with the 3.3-k  resistor and has an equivalent resistance R eq. We want the circuit with and without the voltmeter to be as close as possible. Thus we want R eq to be close to 3.3 k . This is accomplished in R v is very large.

8. PHY 202 (Blum)8 Ammeter Devices in series have the same current. Ammeters are placed in series with a circuit element, so they will experience the same current as it.

9. PHY 202 (Blum)9 R A should be small R eq = (R A + R 1 + R 3.3 ) If R A  0 R eq  (R 1 + R 3.3 ) Ammeters should have small resistances The ammeter is in series with the 1- and 3.3-k  resistors. For the ammeter to have a minimal effect on the equivalent resistance, its resistance should be small.

10. PHY 202 (Blum)10 Simplifying circuits using series and parallel equivalent resistances

11. PHY 202 (Blum)11 Analyzing a combination of resistors circuit Look for resistors which are in series (the current passing through one must pass through the other) and replace them with the equivalent resistance (R eq = R 1 + R 2 ). Look for resistors which are in parallel (both the tops and bottoms are connected by wire and only wire) and replace them with the equivalent resistance (1/R eq = 1/R 1 + 1/R 2 ). Repeat as much as possible.

12. PHY 202 (Blum)12 Look for series combinations R eq =3k  R eq =3.6 k 

13. PHY 202 (Blum)13 Look for parallel combinations R eq = 1.8947 k  R eq = 1.1244 k 

14. PHY 202 (Blum)14 Look for series combinations R eq = 6.0191 k 

15. PHY 202 (Blum)15 Look for parallel combinations R eq = 2.1314 k 

16. PHY 202 (Blum)16 Look for series combinations R eq = 5.1314 k 

17. PHY 202 (Blum)17 Equivalent Resistance I = V/R = (5 V)/(5.1314 k  ) = 0.9744 mA

18. PHY 202 (Blum)18 Kirchhoff’s Rules When series and parallel combinations aren’t enough

19. PHY 202 (Blum)19 Some circuits have resistors which are neither in series nor parallel They can still be analyzed, but one uses Kirchhoff’s rules.

20. PHY 202 (Blum)20 Not in series The 1-k  resistor is not in series with the 2.2-k  since the some of the current that went through the 1-k  might go through the 3-k  instead of the 2.2-k  resistor.

21. PHY 202 (Blum)21 Not in parallel The 1-k  resistor is not in parallel with the 1.5-k  since their bottoms are not connected simply by wire, instead that 3-k  lies in between.

22. PHY 202 (Blum)22 Kirchhoff’s Node Rule A node is a point at which wires meet. “What goes in, must come out.” Recall currents have directions, some currents will point into the node, some away from it. The sum of the current(s) coming into a node must equal the sum of the current(s) leaving that node. I 1 + I 2 = I 3 I 1   I 2  I 3 The node rule is about currents!

23. PHY 202 (Blum)23 Kirchhoff’s Loop Rule 1 “If you go around in a circle, you get back to where you started.” If you trace through a circuit keeping track of the voltage level, it must return to its original value when you complete the circuit Sum of voltage gains = Sum of voltage losses

24. PHY 202 (Blum)24 Batteries (Gain or Loss) Whether a battery is a gain or a loss depends on the direction in which you are tracing through the circuit Gain Loss Loop direction

25. PHY 202 (Blum)25 Resistors (Gain or Loss) Whether a resistor is a gain or a loss depends on whether the trace direction and the current direction coincide or not. II LossGain Loop direction Current direction

26. PHY 202 (Blum)26 Neither Series Nor Parallel I 1  I 2.2  I 1.5  I 1.7  I 3  Draw loops such that each current element is included in at least one loop.

27. PHY 202 (Blum)27 Apply Current (Node) Rule I 1  I 1 -I 3  I 1.5  I 1.5 +I 3  I 3  *Node rule applied. **

28. PHY 202 (Blum)28 Three Loops Voltage Gains = Voltage Losses 5 = 1 I 1 + 2.2 (I 1 – I 3 ) 1 I 1 + 3 I 3 = 1.5 I 1.5 2.2 (I 1 – I 3 ) = 3 I 3 + 1.7 (I 1.5 + I 3 ) Units: Voltages are in V, currents in mA, resistances in k 

29. PHY 202 (Blum)29 Simplified Equations 5 = 3.2 I 1 - 2.2 I 3 I 1 = 1.5 I 1.5 - 3 I 3 0 = -2.2 I 1 + 1.7 I 1.5 + 6.9 I 3 Substitute middle equation into others 5 = 3.2 (1.5 I 1.5 - 3 I 3 ) - 2.2 I 3 0 = -2.2 (1.5 I 1.5 - 3 I 3 ) + 1.7 I 1.5 + 6.9 I 3 Multiply out parentheses and combine like terms.

30. PHY 202 (Blum)30 Solving for I 3 5 = 4.8 I 1.5 - 11.8 I 3 0 = - 1.6 I 1.5 + 13.5 I 3 Solve the second equation for I 1.5 and substitute that result into the first 5 = 4.8 (8.4375 I 3 ) - 11.8 I 3 5 = 28.7 I 3 I 3  0.174 mA

31. PHY 202 (Blum)31 Comparison with Simulation

32. PHY 202 (Blum)32 Other currents Return to substitution results to find other currents. I 1.5 = 8.4375 I 3 = 1.468 mA I 1 = 1.5 I 1.5 - 3 I 3 I 1 = 1.5 (1.468) - 3 (0.174) I 1 = 1.68 mA

33. PHY 202 (Blum)33 Power Recall Voltage = Energy/Charge Current = Charge/Time Voltage  Current = Energy/Time The rate of energy per time is known as power. It comes in units called watts.

34. PHY 202 (Blum)34 Power differences for elements in “Equivalent” circuits Resistor dissipates 100 mW Resistor dissipates 25 mW Same for circuit but different for individual resistors

35. PHY 202 (Blum)35 Power supplies Supplies power to a computer Transforms 120 V (wall socket voltage) down to voltages used inside computer (12 V, 5 V, 3.3 V). Converts the AC current to DC current (rectifies). Regulates the voltage to eliminate spikes and surges typical of the electricity found in average wall socket. Sometimes needs help in this last part, especially with large fluctuations.

36. PHY 202 (Blum)36 Power supply Power supplies are rated by the number of watts they provide. The more powerful the power supply, the more watts it can provide to components. For standard desktop PC, 200 watts is enough Full Towers need more The more cards, drives, etc., the more power needed

37. PHY 202 (Blum)37 Surge protection Takes off extra voltage if it gets too high (a surge). Must be able to react quickly and take a large hit of energy. They are rated by the amount of energy they can handle. I read that one wants at least 240 Joules

38. PHY 202 (Blum)38 Voltage regulator Most PC’s power supplies deliver 5 V, but most processors need a little less than 3.5 V. A voltage regulator reduces the voltage going into the microprocessor. Voltage regulators generate a lot of heat, so they are near the heat sink.

39. PHY 202 (Blum)39 VRM/VID Voltage Regulator Module: a small module that installs on a motherboard to regulate the voltage fed to the microprocessor. It’s replaceable Voltage ID (VID) regulators are programmable; the microprocessor tells the regulator the correct voltage during power- up.

40. PHY 202 (Blum)40 UPS Uninterruptible Power Supply, a power supply that includes a battery to continue supplying power during a brown-outs and power outages Line conditioning A typical UPS keeps a computer running for several minutes after an outage, allowing you to save and shut down properly Recall the data in RAM is volatile (needs power)

41. PHY 202 (Blum)41 UPS (Cont.) Some UPSs have an automatic backup/shut-down option in case the outage occurs when you're not at the computer.

42. PHY 202 (Blum)42 SPS Standby Power System: checks the power line and switches to battery power if it detects a problem. The switch takes time (several milliseconds – that’s thousands if not millions of clock cycles) during the switch the computer gets no power. A slight improvement on an SPS is the “Line- interactive UPS” (provides some conditioning)

43. PHY 202 (Blum)43 On-line An on-line UPS avoids these switching power lapses by constantly providing power from its own inverter, even when the power line is fine. Power (AC)  Battery (DC) through inverter (back to AC) On-line UPSs are better but much more expensive

44. PHY 202 (Blum)44 Laser printers and UPS Don’t put a laser printer on a UPS Laser printers can require a lot of power, especially when starting, they probably exceed the UPS rating