Technician Question of the Week T5D02 Voltage Calculation

T5D02: What formula is used to calculate voltage in a circuit?

A. Voltage (E) equals current (I) multiplied by resistance (R)
B.Voltage (E) equals current (I) divided by resistance (R)
C. Voltage (E) equals current (I) added to resistance (R)
D. Voltage (E) equals current (I) minus resistance (R)

At HamRadioSchool.com we’re big fans of the water analogy of electricity. Let’s use the water analogy to think about this question. This question is a statement of Ohm’s Law, E=IR, but let’s think of it as the Plumbing Law.

The electromotive force (EMF, or E) is measured as voltage, and voltage is like water pressure. Think of it as the force or push behind electric current flow. High voltage, like high water pressure, pushes lots of current. Low water pressure results in a small dribble.

The current (I) is measured in amperes, or “amps.” Just as water current is the volume of water molecules flowing down a river or through a pipe, electrical current may be considered as the volume of electrons flowing through a circuit.

Resistance (R) is the opposition to the flow of current. With water in a pipe resistance is encountered when an obstacle is in the flow, perhaps marbles placed in the pipe. Resistance is also encountered when the water current has to do some work, such as turning a waterwheel. Resistance may also be imposed by a narrowing of the pipe so that the water current has to squeeze into a smaller diameter of flow.

Now let’s apply the Plumbing Law. Suppose you are washing the car using a water hose, a steady current (I) flowing out of the hose with no spray nozzle attached. Now you want to increase the water pressure (E) so that you can spray off the soap and possibly douse your little brother as a bonus. How can you do it?

One way you can do it is to increase the resistance (R) at the end of the hose. You place your thumb over the end of the hose, reducing the size of the area through which the current (I) has to flow through. The water pressure (E) is instantly increased by the increased resistance, and you surprise your brother easily with a good soaking thanks to the greater range provided by the increased pressure! A similar result is achieved using a spray nozzle that may be even more effective at increasing the resistance (R).

Another way to increase the pressure (E) is to stroll over to the spigot and open it wider to increase the water current (I) flowing through the hose. Now the flow of current (I) is a greater volume, and another application of your thumb or a nozzle produces an even higher pressure stream that allows you to reach your little brother even as he runs away screaming! Fun!

So, to get higher pressure, or voltage (E), you need either higher current (I) flow, higher resistance (R), or both. The net effect on electrical voltage is multiplicative. Let’s examine the response options, bottom up.

  • D. Voltage (E) equals current (I) minus resistance (R): This does not fit the Plumbing Law. It makes no sense to subtract the resistance from the current. Even if you could, you would get a lower value of voltage as resistance becomes larger, and that does not fit the little brother spraying scenario in which greater resistance provided greater pressure. This ain’t it.
  • C. Voltage (E) equals current (I) added to resistance (R): This one almost makes sense, but uses addition instead of multiplication. Yes, increasing the resistance or increasing the current will provide greater voltage pressure, but to add two quantities you must have identical units of measure. (That is not the case with multiplication or division, however!) This ain’t it either.
  • B. Voltage (E) equals current (I) divided by resistance (R): Close, but no cigar. Think of it this way… If resistance increases you will be dividing by a larger value. If you divide by a larger value the laws of mathematics always give you a smaller result. So this equation is stating that the pressure (E) will decrease if the resistance (R) increases, and we proved the opposite of that by spraying little brother with a thumb over the end of the hose to increase resistance. Increased voltage results from increased resistance, not the other way around. Three down.
  • A. Voltage (E) equals current (I) multiplied by resistance (R): Aha! This one makes sense. An increased pressure (E) will result from increasing either current (I) or resistance (R), and we’re multiplying so the units of current and resistance do not have to match. We illustrated these effects by opening the spigot (increased current) and by reducing the hose area (thumb or nozzle at the end). And doing them both gives greater spraying reach due to the significantly increased water pressure resulting from multiplying them together. Run brother, run!

The answer to Technician question T5D02, “What formula is used to calculate voltage in a circuit?” is A: Voltage (E) equals current (I) multiplied by resistance (R).

Related Question: T5D01, T5D03 through T5D12.