I can learn to resist
Anything but temptation.
I can learn to resist
Anything but frustration.
You can fight
Without ever winning
But never ever win
Without a fight.

("Resist," by Rush, 1996)

https://www.youtube.com/watch?v=WZEJ4OJTgg8

 

THE INTERGALLACTIC SPECIES "THE BORG" ARE WRONG

(Electrical) Resistance IS NOT Futile!

Furthermore ...

(Electrical) Resistance CAN BE ASSIMILATED to work for humankind!

 

For example, electrical resistance makes it possible to toast bread in a toaster!

 

 

And electrical resistance makes it possible to light up an incandescent light bulb!

 

A Variable Resistor can vary the current to create a dimmer-switch light.

 

 

So the alien species known as "The Borg" were wrong:

Resistance is Not Futile ...

because it can be usefully assimilated into electric circuits.

And at the processing facility, electrical resistance can be used to measure the Process Variable Temperature!

 

OHHMMM

PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order already rocked down to Electric Avenue back in PTOA Segment #106.

 

So PTOA Readers and Students are already aware that:

Electrical resistance can be generated by inserting an electronic component called a Resistor  into an electrical circuit.

The purpose of the Resistor is to control the flow of current through the circuit.

 

The circuit shown in the nearby schematic is powered by a battery (labelled Cell).

The current flows out of the battery through an ammeter (Circle with an 'A')  that measures current.

Then the current flows through a Resistor and a Rheostat.

A Voltmeter (V) measures the voltage drop before and after the fixed Resistor.

Electrical resistance is represented as a jagged line in an electrical circuit.

A "Variable Resistor" (aka rheostat) is represented as a jagged line with an arrow through it.

Electrical resistance is represented as the letter "R" in Ohm's Law.

Electrical resistance is measured in ohms...

and ohms are equal to volts divided by amperes...

because rearranging Ohm's Law defines the mathematical expression

R = V / I.

 

CLOSER SCRUTINY OF THE ROLE RESISTANCE PLAYS IN OHM'S LAW 

In the next few paragraphs, PTOA Readers and Students will analyze graphs of Ohm's Law to deduce interesting relationships between Volts, Current, and Resistance.

The methods used to analyze the graphs can be universally applied to understand all the graphs that appear in the PTOA from here on!

As stated above, one form of Ohm's Law is:

 R=V/I

All PTOA Readers and Students know that the above mathematical expression is just a definition for Resistance (R).

Resistance (R) is defined by dividing Voltage (V)  by  Current (I).

The linear relationship of Ohm's Law is visually revealed when Volts (V) of a circuit are plotted on the Y axis of a graph and the Current (I, in Amperes) of the circuit are plotted on the X axis of the graph as is shown below.

From math class graphing exercises, PTOA Readers and Students probably remember that slope means "how fast the curve moves up the Y scale compared to how fast the curve runs across the the X scale."

Determining the slope at any point on the curve is possible  by dividing the Y axis value with its corresponding X axis value.

That's why slope was also sometimes called "rise-over-run" in math classes.

Hey!

That must mean that the slope of the curve plotted in the Ohm's Law graph also represents the Resistance in an electrical circuit because:

Rise/Run = Y/X = Volts/Current = Resistance!

Yes Indeedo!

The slope in the nearby graph visually represents the Resistance for the two circuits shown as A and B.

PTOA Readers and Students should observe that the steeper slope of circuit A  means there is more electrical resistance in that circuit compared to the resistance of circuit B.

PTOA Readers and Students should also notice that the lines that represent the slopes of both Circuit A and Circuit B are very straight lines.

Those very straight lines inform PTOA Readers and Students that the magnitude of Resistance is very constant throughout the range of measured current (I, in Amperes).

I'll just bet Fred is  a little confused at this point.

Yup, he is.

So Fred needs to focus on the below graph that shows two different lines with two different slopes.

The red line in the nearby graph is "mostly linear" but has a change in slope that is very noticeable.

Throughout the range of temperatures measured, the red line in the nearby graph:

• Starts out at 0 °C with one slope.
• Changes in the middle (from 500 to 1500 °C) to less "rise/run."
• Returns to the originally observed slope above 1500 °C.

The blue line in the above graph and the two lines that characterize the two different currents of Ohm's Law in the graph to the right have very constant slopes and therefore are very straight lines.

Ergo, the relationship between Volts, Amps, and Ohms (Resistance) is very linear throughout the range of measured current (I, in amperes) shown on the graph.

Why do we care about this extremely linear relationship?

What are the chances the extreme linearity of electrical resistance can be used to measure the process variable temperature?

 

FUNNY THINGS ABOUT OHMS

1.The shorthand for the units of current are amps = A.  That makes sense.

The shorthand for the units of voltage are volts = V. That makes sense.

However...The shorthand for the units of electrical resistance ... ohms = the capitalized Greek letter Omega, which looks like a horse shoe with feet:  Ω

Yes, Fred ... a horse shoe with feet:  Ω

2. But what does ohm ... upside down horse shoe with feet ... mean in the real world?

The PTOA Department of Redundancy Department repeats the statement that was made above:

The purpose of the Resistor is to control the flow of current through the circuit

A typical 100 W incandescent light bulb in an electrical circuit has an electrical resistance of 100 Ωs.

 

 

A typical toaster has a signficantly lower resistance of 15 to 20 Ωs.

 

It doesn't seem quite right to the ear at first ... but when two circuits are in the same room and the same ambient temperature ...

The LOWER the electrical resistance in an electrical circuit the GREATER the current (I) and therefore amps (A) flowing through the circuit.

The circuit shown in the graphic to the left has just one 10 kΩ resistor and the current is 1.0 mA.

 

 

Another 10 kΩ resistor is placed in series with the first resistor.

Now the current flows through one 10 kΩ resistor and then flows directly into the second  10 kΩ resistor.

The total resistance for the circuit 20 kΩ.

Otherwise both circuits are identical with respect to  wire type and gauge, voltage, and ambient conditions.

Note that the circuit that has an increase resistance of 20 kΩ has reduced current to 0.5 mA.

Hey!

The same result is seen in the graphs of Ohm's Law!

(Remember that Resistance is the slope of each line).

Circuit A at 5 Volts has current of 1 amp and a Resistance of 5/1= 5Ω.

Circuit B at 5 Volts has a current of 8 amps and a Resistance of 5/8 = 0.625Ω.

 

RESISTANCE-TEMPERATURE DETECTORS (RTDs)

All PTOA Readers and Students know by now that thermocouples have a "pretty darn good, mostly linear" relationship with temperature changes.

Well, it ends up that Resistance-Temperature Detectors (RTDs) and thermistors have a very strong linear relationship with temperature.

RTDs and thermistors generate output in units of resistance (ohms) that can be very accurately correlated to temperature over and over again with no degradation in measurement.

From what PTOA Readers and Students have learned in this PTOA Segment #113, it is not hard to imagine why the metals chosen to make RTDs must have:

• A very linear resistance-to-temperature relationship.
• The ability to correct for the ohms that are self-generated in the circuitry as was explained above because these self-generated ohms have nothing to do with measuring a process temperature.
• A means to convert the corrected ohms generated by temperature changes only into a standard signal millivolt output that can then be transmitted into a DCS field component or into the control board in the control room.

Want to learn more about how RTDs measure temperature? The next PTOA Segment #114 will Make It So.

Captain Picard is looking much more human, don't you think?

 

TAKE HOME MESSAGES: The relationship between Voltage, Current, and Resistance described by Ohm's Law is an example of an extremely linear real-world relationship that predicts how a simple circuit will behave. 

Using the example of an Ohm's Law graph, PTOA Readers and Students analyzed a graphic of a linear relationship.The same analytical approach should be used when studying graphs of all types. Ask yourself "What is the slope and how does it change?"

Resistance is measured in Ohms. The symbol for Ohms is Ω.

Electrical Resistance is added into an electrical circuit by adding in the electronic component known as a Resistor.

A Resistor is represented as a jagged line in a circuit. A jagged line with an arrow through it is a Variable Resistor.

The purpose of the Resistor in an electrical circuit is to control the flow of current through the circuit,

The greater the current in circuit, the less electrical resistance in the circuit.

Analogous to thermocouples, RTDs and thermistors have a linear relationship between resistance and temperature changes that can be correlated to generate a measured temperature.

A means to correct the generated ohm output for self-circuit heating and converting the ohm output into a standard millivolt output is required to make RTDs operable.

©2016 PTOA Segment 00113
PTOA Process Variable Temperature Focus Study Area
PTOA Process Industry Automation Focus Study Area

 

 

You need to login or register to bookmark/favorite this content.