Voltage, Current, and Resistance

Question 1:

Voltage is commonly defined as ëlectrical pressure." The unit of the volt, however, may be defined in terms of more fundamental physical units. What are these units, and how do they relate to the unit of the volt? 

1 volt is equal to 1 joule of energy imparted to 1 coulomb of charge (6.25 ×10¹⁸ electrons): 

V = W Q

Where, 
V = Voltage (volts) 
W = Work, or potential energy (joules) 
Q = Charge (coulombs) 

Notes:
Note that I use the letter "V" to denote voltage rather than Ë" as I usually do. This is because in general physics work, Ë" usually stands for either Ënergy" or Ëlectric field". Some electronics reference books use the letter Ë" for voltage, while others use the letter "V", or even use the two letters interchangeably. 

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Question 2:

Electric current is measured in the unit of the ampere, or amp. What is the physical definition for this unit? What fundamental quantities constitute 1 ampere of electric current? 

1 ampere of electric current is the rate of electron motion equal to 1 coulomb per second: 

I = Q t

Where, 
I = Electric current (amperes) 
Q = Charge in motion (coulombs) 
t = Time (seconds) 

Notes:
It may be helpful at this point to review the number of electrons constituting one coulomb of charge: 6.25 ×10¹⁸ electrons. 
Technically, current's mathematical definition involves calculus: 

I = dQ dt

However, students at this stage may not be ready to explore derivatives yet, and so the equation give in the answer for (average) current will suffice. 

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Question 3:

Explain what the electrical terms voltage, current, and resistance mean, using your own words. 

Voltage: electrical "pressure" between two different points or locations. 
Current: the flow of electrons. 
Resistance: opposition, or "friction," to the flow of electrons. 

Notes:
While it is easy enough for students to look up definitions for these words from any number of references, it is important that they be able to cast them into their own words. Remembering a definition is not the same as really understanding it, and if a student is unable to describe the meaning of a term using their own words then they definitely do not understand it! It is also helpful to encourage students to give real-life examples of these terms. 

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Question 4:

Describe what ëlectricity" is, in your own words. 

If you're having difficulty formulating a definition for ëlectricity," a simple definition of ëlectric current" will suffice. What I'm looking for here is a description of how an electric current may exist within a solid material such as a metal wire. 

Notes:
This question is not as easy to answer as it may first appear. Certainly, electric current is defined as the "flow" of electrons, but how do electrons "flow" through a solid material such as copper? How does anything flow through a solid material, for that matter? 
Many scientific disciplines challenge our "common sense" ideas of reality, including the seemingly solid nature of certain substances. One of the liberating aspects of scientific investigation is that it frees us from the limitations of direct sense perception. Through structured experimentation and rigorous thinking, we are able to ßee" things that might otherwise be impossible to see. We certainly cannot see electrons with our eyes, but we can detect their presence with special equipment, measure their motion by inference from other effects, and prove empirically that they do in fact exist. 
In this regard, scientific method is a tool for the expansion of human ability. Your students will begin to experience the thrill of "working with the invisible" as they explore electricity and electric circuits. It is your task as an instructor to foster and encourage this sense of wonder in your students' work. 

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Question 5:

What units of measurement are used to express quantities of voltage, current, and resistance? 

•

Voltage is measured in the unit of the volt (V).

•

Current is measured in the unit of the ampere, or amp (A).

•

Resistance is measured in the unit of the ohm (Ω).

Notes:
Like all other physical quantities, there are units of measurement appropriate for specifying electrical quantities. In this sense, the "volt," ämp," or öhm" are no different from "gram," ÿard," or "bushel." 

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Question 6:

How many physical points must be referenced when speaking of the following electrical quantities? 

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Voltage

•

Current

•

Resistance

In other words, does it make sense to speak of voltage at a single point, or between two points, or between three points, etc.? Does it make sense to speak of current at a single point, between two points, between three points, etc.? 

•

Voltage is always measured between two points.

•

Current may be measured at a single point (at a cross-section of a conductive path).

•

Resistance is always measured between two points.

Follow-up question: explain, if you can, the relevance of these facts to electrical safety. For example, why is it important to know that voltage is always a quantity existing between two points (rather than existing at a single point) when considering your personal safety? 

Notes:
One of the more confusing aspects of electrical theory is that both voltage and resistance are quantities relative between two points. It is meaningless to speak of the amount of voltage ät this point" in a circuit, at least without implying a reference point such as ground. The same goes for resistance: it makes no sense to speak of how much electrical resistance there is ät this point" in a circuit either. 
Conversely, it makes perfect sense to speak of either voltage or resistance lying "between this point and that point," because both these quantities are relative between exactly two points. 
Current, on the other hand, is the coordinated motion of electric charge through a conductor. As such, it may be measured at any single point in a circuit, like measuring the flow of water in a river at any one particular cross-sectional sample. 

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Question 7:

Lightning is a natural, electrical phenomenon. It is caused by the accumulation of a large electrical charge over time resulting from air, dust, and water droplets transporting small electrical charges. 
Explain how the terms voltage, current, and resistance relate to the process of lightning. In other words, use these three terms to explain the cycle of charge accumulation and lightning discharge. 

As electric charges accumulate between clouds and earth, the voltage between these points increase. Air under normal conditions is a good insulator of electricity: that is, it possesses very high electrical resistance. So, at first there is no current resulting from the rise in voltage between clouds and earth. However, when the voltage exceeds the air's ïonization" potential, the air becomes a good conductor of electricity (its electrical resistance decreases dramatically), resulting in a transient current as the accumulated electric charge dissipates in the form of a lightning bolt. 

Notes:
I usually avoid spending a lot of time on technical definitions, because undue emphasis on the definitions of words tends to reinforce rote memorization rather than true comprehension. If students must master certain definitions, though, it is best to develop that mastery in the context of application: ask the students to use their new vocabulary, not just recite it. 

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Question 8:

Is it possible to have a condition where an electrical voltage exists, but no electric current exists? Conversely, is it possible to have a condition where an electric current exists without an accompanying voltage? Explain your answers, and give practical examples where the stated conditions are indeed possible. 

It is not only possible, but quite common in fact, to have a condition of voltage with no current. However, the existence of an electric current must normally be accompanied by a voltage. Only in very unique conditions (in ßuperconducting" circuits) may an electric current exist in the absence of a voltage. 

Notes:
This question challenges students' comprehension of voltage and current by asking them to explain the relationship between the two quantities in practical contexts. Do not allow students to simply give a ÿes" or a "no" answer to either of the stated conditions. Encourage them to think of examples illustrating a possible condition. 
The term ßuperconducting" may spur some additional questions. As usual, do not simply tell students what superconductivity is, but let them research this on their own. Your more inquisitive students will probably have already researched this topic in response to the answer! 

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Question 10:

Suppose a battery outputs a voltage of 9 volts. Using algebra, calculate how many joules of energy are imparted to every individual electron moving through this battery. 

For a 9 volt battery, there will be 1.44 ×10⁻¹⁸ joules of energy imparted to each electron moving through it. 

Notes:
This problem is another exercise in using scientific notation, and requires that students put concepts together that were learned previously. 

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Question 11:

What is the difference between DC and AC electricity? 

DC is an acronym meaning Direct Current: that is, electrical current that moves in one direction only. AC is an acronym meaningAlternating Current: that is, electrical current that periodically reverses direction (älternates"). 
It is important to realize that "DC" and ÄC" may also be used to represent voltage as well as current. That is, it is possible to have a voltage that alternates back and forth in polarity (ÄC" voltage) just as it is possible to have a current that alternates back and forth in direction of motion. 

Notes:
Though it may seem oxymoronic to refer to either "DC" or ÄC" voltage (Direct Current voltage, or Alternating Current voltage - "current voltage"?), the usage of these acronyms as such is commonplace.