More basic electricity

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

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 (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

Look for series combinations

Look for parallel combinations

Look for series combinations

Look for parallel combinations

Look for series combinations

Equivalent Resistance

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

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.

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

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 voltmeter the resistors are in series

Non-Ideal Voltmeter Ideally the voltmeter should not affect

current in resistor Think of voltmeter as a resistor

RV should be large

If Rv , then

Voltmeters should have large resistances

1=

1+

1Req R3.3 Rv

1

1Req R3.3

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

RA should be small Req = (RA + R1 + R3.3 ) If RA 0 Req (R1 + R3.3 ) Ammeters should have small resistances

Some circuits have resistors which are neither in series nor parallel

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

Kirchhoff’s Node Rule What goes in, must come out The current(s) coming into a node must

equal the current(s) leaving that node I1 + I2 = I3

I1 I2

I3

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

Voltage gains = Voltage losses

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

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

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.

Apply Current (Node) Rule

I1

I1-I3

I1.5

I1.5+I3

I3

*Node rule applied.

* *

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) Voltages are in V, currents in mA,

resistances in k

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

Solving for I3

5 = 4.8 • I1.5 - 11.8 • I3

0 = - 1.6 I1.5 + 13.5 • I3

Substitute the second into the first 5 = 4.8 • (8.4375 I3 ) - 11.8 • I3

5 = 28.7 • I3

I3 0.174 mA

Comparison with Simulation

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

Power differences in “Equivalent” circuits

Resistor dissipates 100 mW

Resistor dissipates 25 mW

Same for circuit but different for individual resistors

Power supplies Supplies power to a computer Transforms 120 V 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

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

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

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

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.

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)

UPS (Cont.) Some UPSs have an automatic

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

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)

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

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