Ohm’s Law Worksheet

Students may find a basic physics text helpful in obtaining these definitions. “Work” is a difficult concept to precisely define, especially for students unfamiliar with basic physics. Technically, it is the vector dot-product of force and displacement, meaning that work equals force times distance only if the force and distance vectors are precisely parallel to each other. In other words, if I carry a 10 kg mass (lifting up against the tug of gravity) while walking parallel to the ground (not going up or down), the force and displacement vectors are perpendicular to each other, and the work I do in carrying the mass is zero. It is only if my force is directed precisely the same direction as my motion that all of my effort is translated into work.

Note that I use the letter “V” to denote voltage rather than “E” as I usually do. This is because in general physics work, “E” usually stands for either “Energy” or “Electric field”. Some electronics reference books use the letter “E” for voltage, while others use the letter “V”, or even use the two letters interchangeably.

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:

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.

Water flow is not a perfect analogy for electricity, but is close enough to be useful in basic electricity education. Be prepared to discuss the inadequacies of water as an analogy with your students (i.e. “How come electrons don’t spill out the end of an open wire like water spills out the end of an open hose or pipe?”).

The raw data figures were made intentionally “noisy” in this problem to simulate the types of measurement errors encountered in real life. One tool which helps overcome interpretational problems resulting from noise like this is graphing. Even with noise present, the linearity of the function is quite clearly revealed.

Your students should learn to make graphs as tools for their own understanding of data. When relationships between numbers are represented in graphical form, it lends another mode of expression to the data, helping people to apprehend patterns easier than by reviewing rows and columns of numbers.

Just a simple Ohm’s Law calculation here - no tricks! The point of this question, however, is to get students to think about the steps they follow in doing the calculation. Many students simply wish to memorize procedures rather than learn why to do what they need to do to answer such questions. It is your task as the instructor to challenge them beyond memorization, and through to understanding.

Students need to become comfortable with graphs, and creating their own simple graphs is an excellent way to develop this understanding. A graphical representation of the Ohm’s Law function allows students another “view” of the concept, allowing them to more easily understand more advanced concepts such as negative resistance.

If students have access to either a graphing calculator or computer software capable of drawing 2-dimensional graphs, encourage them to plot the functions using these technological resources.

I have found it a good habit to “sneak” mathematical concepts into physical science courses whenever possible. For so many people, math is an abstract and confusing subject, which may be understood only in the context of real-life application. The studies of electricity and electronics are rich in mathematical context, so exploit it whenever possible! Your students will greatly benefit.

Some students might not realize that in Europe, commas are used as decimal points and visa-versa. Thus, two thousand seven hundred would be written as 2,700 in America and 2.700 in Europe. Conversely, the number π would be written as 3.141593 in America but 3,141593 in Europe. Confusing? Yes!!

As an instructor, I was very surprised to hear many beginning students claim that all current would go through the lesser resistor, and none through the greater resistor! The proverb about “takes the path of least resistance” really should be understood as “proportionately taking paths of lesser resistance.” People new to the study of electricity often misunderstand such basic principles, their errors usually based on folk wisdom like this. It is imperative to break through these myths with hard fact. In this case, Ohm’s Law serves as a mathematical tool we can use to dispel false ideas.

Of course, a circuit as simple as this may be readily assembled and tested in class, so that all may see the truth for themselves.

Many types of electrical and electronic components experience changes in electrical resistance over their operating ranges of current and voltage. Resistors, while simple to study, do not exhibit the behavior of most electronic components. It is important for students to understand that the real world of electricity and electronics is much more complex than what Ohm’s Law might suggest (with an implicit assumption of fixed resistance). This is one concept that graphs really help to illustrate.

One of my goals as a technical educator is to encourage the development of experimentation skills in my students. The most accurate way to gain knowledge of a device’s operation or of an electrical principle is to build a circuit that actually tests it. I’ve used this technique many times in my career to further my knowledge on a subject, and it has proven to be an invaluable skill.

In this question, students are implicitly asked to identify several key things:

• Where to connect a meter to measure lamp voltage.

• Where to connect a meter to measure lamp current.

• How to make the current adjustable, so that multiple values may be tested and plotted.

Additionally, the students must identify what voltage/current ranges will be necessary to test a gas-discharge lamp. Notice the high-voltage power source shown in the schematic diagram. Students may ask “How high must this voltage be?” upon seeing the schematic in the answer. Don’t tell them outright. Rather, have them do some research and report the next day on typical lamp voltages!

Not only do many gas-discharge devices exhibit negative resistance over certain portions of their operating range, but many semiconductor devices do as well.

This is a good starting point for a discussion on work, energy, and power. Power, of course, may be directly calculated by multiplying voltage by current, and is measured in watts. It also provides an opportunity to discuss some of the practical limitations of electrical conductors.

This question is designed to make students think qualitatively about the relationship between current, resistance, and power. I have found that qualitative (non-numeric) analysis is often more challenging than asking students to calculate answers quantitatively (with numbers). Often, simple math is a kind of barrier behind which students seek refuge from true understanding of a topic. In other words, it is easier to punch keys on a calculator (or even perform calculations with paper and pencil) than to really think about the inter-relationships of variables in a physical problem. Yet, a qualitative understanding of electrical systems is vital to fast and efficient troubleshooting.

Students need to become comfortable with graphs, and creating their own simple graphs is an excellent way to develop this understanding. A graphical representation of the Ohm’s Law (actually, Joule’s Law) power function allows students another “view” of the concept.

If students have access to either a graphing calculator or computer software capable of drawing 2-dimensional graphs, encourage them to plot the functions using these technological resources.

The “obvious” solution is a direct application of Ohm’s Law. Other solutions may not be so direct, but they will all relate back to Ohm’s Law somehow.

Algebra is an extremely important tool in many technical fields. One nice thing about the study of electronics is that it provides a relatively simple context in which fundamental algebraic principles may be learned (or at least illuminated).

The same may be said for calculus concepts as well: basic principles of derivative and integral (with respect to time) may be easily applied to capacitor and inductor circuits, providing students with an accessible context in which these otherwise abstract concepts may be grasped. But calculus is a topic for later worksheet questions . . .

The answers to this question should not create any surprises, especially when students understand electrical resistance in terms of friction: resistors with greater resistance (more friction to electron motion) require greater voltage (push) to get the same amount of current through them. Resistors with greater resistance (friction) will also dissipate more power in the form of heat, given the same amount of current.

Another purpose of this question is to instill in students’ minds the concept of components in a simple series circuit all sharing the same amount of current.

Challenge your students to recognize any mathematical patterns in the respective voltage drops and power dissipations. What can be said, mathematically, about the voltage drop across the 2 Ω resistor versus the 1 Ω resistor, for example?

The answers to this question may seem paradoxical to students: the lowest value of resistor dissipates the greatest power. Math does not lie, though.

Another purpose of this question is to instill in students’ minds the concept of components in a simple parallel circuit all sharing the same amount of voltage.

Challenge your students to recognize any mathematical patterns in the respective currents and power dissipations. What can be said, mathematically, about the current drawn by the 2 Ω resistor versus the 1 Ω resistor, for example?

You might want to mention that in electrical parlance, a “heavy” load is one that draws a large amount of current, and thus has a large resistance. This circuit, which shows how the lowest resistance in a parallel circuit consumes the most power, gives practical support to the term “heavy” used to describe loads.

Discuss the concept of energy conservation: that energy can neither be created nor destroyed, but merely changed between different forms. Based on this principle, the sum of all power dissipations in a circuit must equal the total amount of power supplied by the energy source, regardless of how the components are connected together.

Students may have a hard time grasping how a light bulb may be dimmed by turning it on and off really fast. The key to understanding this concept is to realize that the transistor’s switching time must be much faster than the time it takes for the light bulb’s filament to fully heat or fully cool. The situation is analogous to throttling the speed of an automobile by rapidly “pumping” the accelerator pedal. If done slowly, the result is a varying car speed. If done rapidly enough, though, the car’s mass averages the “ON”/“OFF” cycling of the pedal and results in a nearly steady speed.

This technique is very popular in industrial power control, and is gaining popularity as an audio amplification technique (known as Class D). The benefits of minimal wasted power by the control device are many.

This question illustrates a disparity between the ideal conditions generally assumed for theoretical calculations, and those conditions encountered in real life. Truly, it is the purpose of a voltage source to maintain a constant output voltage regardless of load (current drawn from it), but in real life this is nearly impossible. Most voltage sources exhibit some degree of “sag” in their output over a range of load currents, some worse than others.

In this example, it is impossible to tell how much the voltage source’s output will “sag” when the switch is closed, because we have no idea of what the resistor’s current draw will be compared to that of the light bulb, or what the voltage source’s rated output current is. All we can say is that theoretically there will be no effect from closing the switch, but that in real life there will be some degree of dimming when the switch is closed.

Remind students that short-circuit testing of electrical power sources can be dangerous. A student of mine once stuffed a 6-volt “lantern” battery in his tool pouch, only to have it discharge smoke an hour later, after the battery terminals had been shorted together by a wrench handle!

No, Ohm’s Law is not being cheated here: shorting a voltage source with a 0 Ω conductor will not result in infinite current, because there are other sources of resistance in such a circuit. The task here is to determine where those sources might be, and how they could be located.