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More basic electricity

Non-Ideal meters, Kirchhoff’s rules, Power, Power supplies

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What makes for ideal voltmeters and

ammeters?

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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.

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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.

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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.

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Non-Ideal Voltmeter Ideally the voltmeter should not

affect current in resistor. Let us focus on the resistance of

the voltmeter.

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RV should be large

If Rv , then

Voltmeters should have large resistances.

1 = 1 + 1Req R3.3 Rv

1

1Req R3.3

The voltmeter is in parallel with the 3.3-k resistor and has an equivalent resistance Req.

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.

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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.

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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.

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Simplifying circuits using series and parallel equivalent

resistances

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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.

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Look for series combinations

Req=3k

Req=3.6 k

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Look for parallel combinations

Req = 1.8947 k

Req = 1.1244 k

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Look for series combinations

Req = 6.0191 k

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Look for parallel combinations

Req = 2.1314 k

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Look for series combinations

Req = 5.1314 k

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Equivalent Resistance

I = V/R = (5 V)/(5.1314 k) = 0.9744 mA

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Kirchhoff’s Rules

When series and parallel combinations aren’t enough

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Some circuits have resistors which are neither in series nor

parallel

They can still be analyzed, but one uses Kirchhoff’s rules.

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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.

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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.

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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 I1 I2

I3The node rule is about currents!

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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

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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

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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

Loss Gain

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Neither Series Nor Parallel

I1

I2.2

I1.5

I1.7

I3

Draw loops such that each current element is included in at least one loop.

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Apply Current (Node) Rule

I1

I1-I3

I1.5

I1.5+I3

I3

*Node rule applied.

* *

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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

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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.

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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

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Comparison with Simulation

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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

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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.

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Power differences for elements in “Equivalent”

circuits

Resistor dissipates 100 mW

Resistor dissipates 25 mW

Same for circuit but different for individual resistors

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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.

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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

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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

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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.

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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.

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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)

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UPS (Cont.) Some UPSs have an automatic

backup/shut-down option in case the outage occurs when you're not at the computer.

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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)

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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

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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