## Posts Tagged ‘resistance’

### Transistors – Voltage Regulation Part V

Sunday, August 19th, 2012
I’m sure you’ve seen the television commercials warning about harmful interactions between prescription medications.  By the same token electronic circuitry can also be adversely affected by certain combinations of electrical components, as we’ll discuss in today’s blog.

Last time we looked at a circuit schematic containing an unregulated power supply.  This power supply was connected to an external supply circuit containing a number of components such as electric relays, buzzers, and lights.  Each of these components has a resistance factor, and combined they have a total resistance of RTotal.  We saw that when RTotal increases, the electrical current, I, decreases, and when RTotal decreases, I increases.

In contrast to this increasing/decreasing activity of the total resistance RTotal,  the fixed internal resistance of the unregulated power supply, RInternal, doesn’t fluctuate.  Let’s explore Ohm’s Law further to see how the static effect of RInternal  combines with the changing resistance present in RTotal to adversely affect the unregulated power supply output voltage, VOutput, causing it to fluctuate.

## Figure 1

In Figure 1 RTotal and RInternal are operating in series, meaning they are connected together like sausage links.  In this configuration their two resistances add together as if they were one larger resistor.

Generally speaking, Ohm’s Law sets out that the current, I, flowing through a resistor in an electrical circuit equals the voltage, V, applied to the resistor divided by the resistance R, or:

I = V ÷ R

In the case of the circuit represented in Figure 1, the resistors RInternal and RTotal are connected in series within the circuit, so their resistances must be added together to arrive at a total power demand.  Voltage is applied to these two resistors by the same voltage source, VDC.  So, for the circuit as a whole Ohm’s Law would be written as:

I = VDC ÷ (RInternal + RTotal)

But, Ohm’s Law can also be applied to individual parts within the circuit, just as it can be applied to a single kitchen appliance being operated on a circuit shared with other appliances.  Let’s see how this applies to our example circuit’s RTotal next week.

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### Transistors – Voltage Regulation Part III

Tuesday, August 7th, 2012
When my daughter was seven she found out about Ohm’s Law the hard way, although she didn’t know it.  She had accidentally bumped into her electric toy train, causing its metal wheels to derail and fall askew of the metal track.  This created a short circuit, causing current to flow in an undesirable direction, that is, through the derailed wheels rather than along the track to the electric motor in the locomotive as it should.

What happened during the short circuit is that the bulk of the current began to follow through the path of least resistance, that of the derailed wheels, rather than the higher resistance of the electric motor.  Electric current, always opportunistic, will flow along its easiest course, in this case the short, thick metal of the wheels, rather than work its way along the many feet of thin metal wire of the motor’s electromagnetic coils.  With its wheels sparking at the site of derailment the train had become an electric toaster within seconds, and the carpet beneath the track began to burn.  Needless to say, mom wasn’t very happy.

In this instance Ohm’s Law was at work, with a decidedly negative outcome.  The Law’s basic formula concerning the toy train would be written as:

### I = V ÷ R

where, I is the current flowing through the metal track, V is the track voltage, and R is the internal resistance of the metal track and locomotive motor, or in the case of a derailment, the metal track and the derailed wheel.  So, according to the formula, for a given voltage V, when the R got really small due to the derailment, I got really big.

But enough about toy trains.  Let’s see how Ohm’s Law applies to an unregulated power supply circuit.  We’ll start with a schematic of the power supply in isolation.

## Figure 1

The unregulated power supply shown in Figure 1 has two basic aspects to its operation, contained within a blue dashed line.  The dashed line is for the sake of clarity when we connect the power supply up to an external circuit which powers peripheral devices later on.  The first aspect of the power supply is a direct current (DC) voltage source, which we’ll call VDC.  It’s represented by a series of parallel lines of alternating lengths, a common representation within electrical engineering.

And like all electrical components, the power supply has an internal resistance, such as discussed previously.  This resistance, notated RInternal, is the second aspect of the power supply, represented   by another standard symbol, that of a zigzag line.

Finally, the unregulated power supply has two output terminals.  These will connect to an external supply circuit through which power will be provided to peripheral devices.  Next time we’ll connect to this external circuit, which for our purposes will consist of an electric relay, buzzer, and light to see how it all works in accordance with Ohm’s Law.

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### Transistors – Voltage Regulation Part II

Sunday, July 29th, 2012
I joined the Boy Scouts of America as a high schooler, mainly so I could participate in their Explorer Scout program and learn about electronics.  I will forever be grateful to the Western Electric engineers who volunteered their personal time to stay after work and help me and my fellow Scouts build electronic projects.  The neatest part of the whole experience was when I built my first regulated power supply with their assistance inside their lab.  But in order to appreciate the beauty of a regulated power supply we must first understand the shortcomings of an unregulated one, which we’ll begin to do here.

Last time we began to discuss how the output voltage of an unregulated power supply can vary in response to power demand, just as when sprinklers don’t have sufficient water flow to cover a section of lawn.  Let’s explore this concept further.

## Figure 1

Figure 1 shows a very basic representation of a microprocessor control system that operates three components, an electric relay (shown in the blue box), buzzer, and light.  These three components have a certain degree of internal electrical resistance, annotated as RR, RB, and RL respectively.  This is because they are made of materials with inherent imperfections which tend to resist the flow of electric current.  Imperfections such as these are unavoidable in any electronic device made by humans, due to impurities within metals and irregularities in molecular structure.  When the three components are activated by the microprocessor chip via field effect transistors, denoted as FET 1, 2 and 3 in the diagram, their resistances are connected to the supply circuit.

In other words, RR, RB, and RL create a combined level of resistance in the supply circuit by their connectivity to it.  If a single component were to be removed from the circuit, its internal resistance would also be removed, resulting in a commensurate decrease in total resistance.  The greater the total resistance, the more restriction there is to current flow, denoted as I.  The greater the resistance, the more I is caused to decrease.  In contrast, if there is less total resistance, I increases.

The result of changing current flow resistance is that it causes the unregulated power supply output voltage to change.  This is all due to an interesting phenomenon known as Ohm’s Law, represented as this within engineering circles:

V = I × R

where, V is the voltage supplied to a circuit, I is the electrical current flowing through the circuit, and R is the total electrical resistance of the circuit.  So, according to Ohm’s Law, when I and R change, then V changes.

Next time we’ll apply Ohm’s Law to a simplified unregulated power supply circuit schematic.  In so doing we’ll discover the mathematical explanation to the change in current flow and accompanying change in power supply output voltage we’ve been discussing.

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### Wire Size and Electric Current – Joule Heating

Sunday, March 20th, 2011
 Ever take a peek inside the toaster while you’re waiting for the toast to pop up?  If so, you would have noticed a bright orange glow.  That glow is produced when the toasting wires heat up, which in turn creates a nice crusty surface on your bread or waffle.  It’s the same phenomenon as when the filament inside an incandescent bulb glows.  The light and heat produced in both these cases are the result of the Joule, pronounced “jewel,” effect at work.      To understand Joule heating, let’s first refresh our memories as to electrical current resistance.  We learned previously that wire is not a perfect conductor, and as such resistance to flow is encountered.  This resistance causes power to be lost along the length of wire, in accordance with this equation: Power Loss = I2 × R Where I is the electric current flowing through a wire, and R is the total electrical resistance of the wire.  The power loss is measured in units of Joules per second, otherwise known as watts, “watt” denoting a metric unit of power.  It is named after the famed Scottish mechanical engineer, James Watt, who is responsible for inventing the modern steam engine.  A Joule is a metric unit of heat energy, named after the English scientist James Prescott Joule.  He was a pioneer in the field of thermodynamics, a branch of physics concerned with the relationships between different forms of energy.      Anyway, to see how the equation works, let’s look at an example.  Suppose we have 12 feet of 12 AWG copper wire.  We are using it to feed power to an appliance that draws 10 amperes of electric current.  Going to our handy engineering reference book, we find that the 12 AWG wire has an electrical resistance of 0.001588 ohms per foot, “ohm” being a unit of electrical resistance.  Plugging in the numbers, our equation for total electrical resistance becomes: R = (0.001588 ohms per foot) × 12 feet = 0.01905 ohms And we can now calculate power loss as follows: Power = I2 × R = (10 amperes)2 × (0.01905 ohms) = 1.905 watts      Instead of using a 12 AWG wire, let’s use a smaller diameter wire, say, 26 AWG.  Our engineering reference book says that 26 AWG wire has an electrical resistance of 0.0418 ohms per foot.  So let’s see how this changes the power loss: R = (0.0418 ohms per foot) × 12 feet = 0.5016 ohms Power = I2 × R = (10 amperes)2 × (0.5016 ohms) = 50.16 watts      This explains why appliances like space heaters and window unit air conditioners have short, thick power cords.  They draw a lot of current when they operate, and a short power cord, precisely because it is short, poses less electrical resistance than a long cord.  A thicker cord also helps reduce resistance to power flow.  The result is a large amount of current flowing through a superhighway of wire, the wide berth reducing both the amount of power loss and the probability of dangerous Joule heating effect from taking place.       Our example shows that the electric current flowing through the 12 AWG wire loses 1.905 watts of power due to the inconsistencies within the wire, and this in turn causes the wire to heat up.  This is Joule heating at work.  Joule heating of 50.16 watts in the thinner 26 AWG wire can lead to serious trouble.      When using a power cord, heat moves from the copper wire within it, whose job it is to conduct electricity, and beyond, on to the electrical insulation that surrounds it.  There the heat is not trapped, but escapes into the environment surrounding the cord.  If the wire has low internal resistance and the amount of current flowing through it is within limits which are deemed to be acceptable, then Joule heating can be safely dissipated and the wire remains cool.  But if the current goes beyond the safe limit, as specified in the American Wire Gauge (AWG) table for that type of wire, then overheating can be the result.  The electrical insulation may start to melt and burn, and the local fire department may then become involved.          That’s it for wire sizing and electric current.  Next time we’ll slip back into the mechanical world and explore a new topic: the principles of ventilation. _____________________________________________

### Transformers – Electric Utility Power Savers

Sunday, January 2nd, 2011