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More basic electricity

More basic electricity. Non-Ideal meters, Kirchhoff’s rules, Power, Power supplies. What makes for ideal voltmeters and ammeters?. 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.

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More basic electricity

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  1. More basic electricity Non-Ideal meters, Kirchhoff’s rules, Power, Power supplies

  2. What makes for ideal voltmeters and ammeters?

  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. 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. Theoretical calculation • 5 V = (1 k + 3.3 k ) I • 5 V = (4.3 k ) I • I = 1.16279 mA • V3.3 = (3.3 k ) (1.16279 mA) • V3.3 = 3.837 V • Slight discrepancy? Without the voltmeter, the two resistors are in series.

  6. Non-Ideal Voltmeter • Ideally the voltmeter should not affect current in resistor. • Let us focus on the resistance of the voltmeter.

  7. RV should be large The voltmeter is in parallel with the 3.3-k resistor and has an equivalent resistance Req. • If Rv , then • Voltmeters should have large resistances. We want the circuit with and without the voltmeter to be as close as possible. Thus we want Req to be close to 3.3 k. This is accomplished in Rv is very large.

  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. RA should be small • Req = (RA + R1 + R3.3 ) • If RA  0 • Req  (R1 + R3.3 ) • 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. Simplifying circuits using series and parallel equivalent resistances

  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 (Req = R1 + R2). • 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/Req = 1/R1 + 1/R2). • Repeat as much as possible.

  12. Look for series combinations Req=3k Req=3.6 k

  13. Look for parallel combinations Req = 1.8947 k Req = 1.1244 k

  14. Look for series combinations Req = 6.0191 k

  15. Look for parallel combinations Req = 2.1314 k

  16. Look for series combinations Req = 5.1314 k

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

  18. Kirchhoff’s Rules When series and parallel combinations aren’t enough

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

  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. 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. 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. • I1 + I2 = I3  I2 I1   I3 The node rule is about currents!

  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. 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 Loop direction Loop direction Loss Gain

  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. I I Loop direction Loop direction Current direction Current direction Loss Gain

  26. Neither Series Nor Parallel I1.5  I1  I3  I2.2  I1.7  Draw loops such that each current element is included in at least one loop.

  27. Apply Current (Node) Rule I1.5  I1  I3  * * I1-I3  I1.5+I3  *Node rule applied.

  28. Three Loops • Voltage Gains = Voltage Losses • 5 = 1 • I1 + 2.2 • (I1 – I3) • 1 • I1 + 3 • I3 = 1.5 • I1.5 • 2.2 • (I1 – I3) = 3 • I3 + 1.7 • (I1.5 + I3) • Units: Voltages are in V, currents in mA, resistances in k

  29. Simplified Equations • 5 = 3.2 • I1 - 2.2 • I3 • I1 = 1.5 • I1.5 - 3 • I3 • 0 = -2.2 • I1 + 1.7 • I1.5 + 6.9 • I3 • Substitute middle equation into others • 5 = 3.2 • (1.5 • I1.5 - 3 • I3) - 2.2 • I3 • 0 = -2.2 • (1.5 • I1.5 - 3 • I3) + 1.7 • I1.5 + 6.9 • I3 • Multiply out parentheses and combine like terms.

  30. Solving for I3 • 5 = 4.8 • I1.5 - 11.8 • I3 • 0 = - 1.6 I1.5 + 13.5 • I3 • Solve the second equation for I1.5 and substitute that result into the first • 5 = 4.8 • (8.4375 I3 ) - 11.8 • I3 • 5 = 28.7 • I3 • I30.174 mA

  31. Comparison with Simulation

  32. Other currents • Return to substitution results to find other currents. • I1.5 = 8.4375 I3 = 1.468 mA • I1 = 1.5 • I1.5 - 3 • I3 • I1 = 1.5 • (1.468)- 3 • (0.174) • I1 = 1.68 mA

  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. Power differences for elements in “Equivalent” circuits Same for circuit but different for individual resistors Resistor dissipates 100 mW Resistor dissipates 25 mW

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

  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. 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. 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

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