Notes:
This question affords an excellent opportunity to discuss another foundational concept of electricity: that voltage is always measured between two points.

Hide Answer

Notes:
Ask the students how an analog (moving pointer) style of voltmeter would respond in this situation. This question lends itself very well to simple experimentation in the classroom, even during discussion time.

Hide Answer

Notes:
Ask your students why a voltmeter should have a very high resistance (many thousands or millions of ohms) between its test leads. How does this property of all voltmeters relate to how they are used to measured current in real circuits?

Hide Answer

�

Red lead on Ä", black lead on ground (Digital voltmeter reads +15 volts)

�

Red lead on "B", black lead on ground (Digital voltmeter reads -15 volts)

�

Red lead on Ä", black lead on "B" (Digital voltmeter reads +30 volts)

�

Red lead on "B", black lead on Ä" (Digital voltmeter reads -30 volts)

Notes:
This question may be easily answered with only a voltmeter, two batteries, and a single "jumper" wire to connect the two batteries in series. It does not matter if the batteries are 15 volts each! The fundamental principle may still be investigated with batteries of any voltage, so this is a very easy demonstration to set up during discussion time.

Hide Answer

�

Between TB1-1 and TB1-3 (Voltmeter measures 9 volts)

�

Between TB1-4 and TB2-4 (Voltmeter measures 0 volts)

�

Between TB2-3 and TB2-1 (Voltmeter measures 0 volts)

�

Between TB1-1 and TB2-1 (Voltmeter measures 9 volts)

Notes:
This question provides an opportunity to discuss the concept of electrically common points: namely, that there can be no substantial voltage built up between points that are made ëlectrically common" by means of low-resistance connections between them.
This is also an opportunity to develop the skill of drawing a schematic diagram for a real-life circuit. Schematic diagrams, of course, are very helpful in that they provide a nice, neat layout of all circuit components, making visualization of voltage drops and other quantities easier.

Hide Answer

�

Between TB1-1 and TB1-3 (Voltmeter measures 9 volts)

�

Between TB1-4 and TB2-4 (Voltmeter measures 9 volts)

�

Between TB2-3 and TB2-1 (Voltmeter measures 0 volts)

�

Between TB1-1 and TB2-1 (Voltmeter measures 9 volts)

Notes:
Ask your students this question: how does the break in the wire affect electrical "commonality" between TB1-4 and TB2-4?

Hide Answer

�

Voltmeter A = 6 volts

�

Voltmeter B = 0 volts

�

Voltmeter C = 6 volts

�

Voltmeter D = 0 volts

Notes:
Students often find the terms öpen" and "closed" to be confusing with reference to electrical switches, because they sound opposite to the function of a door (i.e. you can only go through an open door, but electricity can only go through a closed switch!). The words actually make sense, though, if you look at the schematic symbol for an electrical switch as a door mounted ßideways" in the circuit. At least visually, then, öpen" and "closed" will have common references.
One analogy to use for the switch's function that makes sense with the schematic is a drawbridge: when the bridge is down (closed), cars may cross; when the bridge is up (open), cars cannot.
I have found that the concept of electrically common points is most helpful when students first learn to relate voltage drop with continuity (breaks or non-breaks) in a circuit.
To be able to immediately relate the expected voltage drop between two points with the electrical continuity between those points is a very important foundational skill in electrical troubleshooting. Without mastery of this skill, students will have great difficulty detecting and correcting faults in circuits caused by poor connections and broken wires, which constitute a fair portion of realistic circuit failures.

Hide Answer

�

Voltmeter A = 0 volts

�

Voltmeter B = 6 volts

�

Voltmeter C = 6 volts

�

Voltmeter D = 0 volts

Notes:
Students often find the terms öpen" and "closed" to be confusing with reference to electrical switches, because they sound opposite to the function of a door (i.e. you can only go through an open door, but electricity can only go through a closed switch!). The words actually make sense, though, if you look at the schematic symbol for an electrical switch as a door mounted ßideways" in the circuit. At least visually, then, öpen" and "closed" will have common references.
One analogy to use for the switch's function that makes sense with the schematic is a drawbridge: when the bridge is down (closed), cars may cross; when the bridge is up (open), cars cannot.
I have found that the concept of electrically common points is most helpful when students first learn to relate voltage drop with continuity (breaks or non-breaks) in a circuit.
To be able to immediately relate the expected voltage drop between two points with the electrical continuity between those points is a very important foundational skill in electrical troubleshooting. Without mastery of this skill, students will have great difficulty detecting and correcting faults in circuits caused by poor connections and broken wires, which constitute a fair portion of realistic circuit failures.

Hide Answer

Notes:
Many multimeters use ïnternational" symbols to label DC and AC selector switch positions. It is important for students to understand what these symbols mean.
The test lead connections (to the circuit) shown are not the only correct answer. It is possible to touch the test leads to different points on the PCB and still measure the voltage across the resistor (R1). However, if there are poor connections on the circuit board (between component leads and copper traces), measuring voltage at points on the circuit board other than directly across the component in question may give misleading measurements. Discuss this with your students.

Hide Answer

Notes:
I always like to have my students begin their test equipment familiarity by using old-fashioned analog multimeters. Only after they have learned to be proficient with an inexpensive meter do I allow them to use anything better (digital, auto-ranging) in their work. This forces students to appreciate what a "fancy" meter does for them, as well as teach them basic principles of instrument ranging and measurement precision.

Hide Answer

Notes:
This is an interesting mathematical exercise, to determine the total number of 2-wire combinations resulting from 15 wires. If your students have difficulty determining this number, suggest they try to figure out the total number of 2-wire combinations with a smaller quantity of wires, say four instead of fifteen.
Incidentally, this is a powerful problem-solving technique: simplify the problem into one with smaller quantities, until the solution becomes intuitively obvious, then determine the precise steps needed to arrive at that obvious solution. After that, apply those same steps to the original problem.
The challenge question is actually pre-calculus or calculus level.

Hide Answer

Notes:
I have found that the concept of "swamping" is extremely useful when making estimations. To be able to ignore the values of some components allows one to simplify a great many circuits, enabling easier calculations to be performed.

Hide Answer