- Stu WØSTU

# Voltage Calculation (T5D02)

The 2022-2026 Technician License question pool asks for the general equation to compute voltage:

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

A. E= I x R

B. E= I / R

C. E= I + R

D. E = I - R

At Ham Radio School we are big fans of the water analogy of electricity. It just make physical sense and it easy to use to imagine how electricity behaves. So, let's use it to think about this question. The question really gets at Ohm's Law which states that in a circuit the electromotive force is equal to the electrical current multiplied by the electrical resistance. Instead, let's think about this as the Plumbing Law.

The electromotive force (EMF, or E) is measured in units of volts, or as *voltage*, and voltage is like the water pressure in the plumbing. Think of voltage as the force or push causing electric current flow, just as water pressure causes the water to flow. High voltage, like high water pressure, compels lots of current to flow. Low water pressure results in a small dribble of current.

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 electrical charges flowing through the circuit.

Resistance (R) is the opposition to the flow of current. With water in a pipe resistance is encountered when there is a constriction of the pipe, perhaps due to a narrowed pipe diameter or due to obstacles in the pipe around which the water must flow. Resistance is also encountered when the water current has to do some work, such as turning a waterwheel. Similarly, electrical appliances that require the current to do some work also impose significant resistance. So, a lightbulb being illuminated and producing some heat is imposing resistance on the circuit in which it resides. A motor turning a propeller on a quad-copter also imposes resistance in the power circuit of the drone.

In a circuit measurement, voltage is referring to the *voltage drop*. That is, the change in the voltage across some appliance or electrical component that imposes some resistance. Let’s apply the Plumbing Law to think about this.

Suppose you are washing your car using a water hose, a steady current (I) flowing out of the hose with no spray nozzle attached. Now you want to 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. The pressure (voltage) in the hose prior to reaching your thumb resistance is high, but the pressure beyond your thumb and outside the hose is low since the constriction is relieved. Thus, a pressure drop occurs as the current flows across the resistance. You may consider that the pressure drop has been converted into the work of spewing the water current a greater distance to rinse the car and to soak little brother.

The analogy with electricity is, of course, that across a resistor or an appliance the voltage will drop. The resistor will convert some electrical power to heat, while an appliance will convert it to work and heat. You can probably imagine with the water analogy that if we increase the resistance, the magnitude of the pressure drop will increase. Similarly, if we increase the current that must flow across the resistance, the pressure drop magnitude will commensurately increase. If we increase both the resistance and current, the effect on voltage is multiplicative.

Now you can easily infer the correct relationship for Ohm's Law and the answer to this question. **"T5D02: What formula is used to calculate voltage in a circuit?"** The answer is 'A', **E = I x R.**

-- Stu WØSTU