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The electric current–water analogy

Electricity and magnetism

The electric current–water analogy

Jay Mantri

The electric current–water analogy

The analogy between electric current in a wire and water flowing through a pipe is perhaps one of the most long-lasting and accurate ones for learners.

In many concepts, understanding comes easily when you visualize it or find a suitable analogy. This article is aimed at creating one such visualization or analogy for electric currents. An analogy is basically a one-to-one relation between a tough-to-understand or new concept to something that is experienced in day-to-day life.

Current electricity isn’t really a concept that is tough to understand, and the following analogy should show the reader why. Let us consider a pipe with water. The pipe is the wire. The water, or rather, the particles of water are the charge carriers, the electrons within the material of the wire.

Current

As mentioned, the molecules of water are the charges within the conductor. In that statement, it is tempting to explore the discreteness of electrons and water molecules, but our aim is to simplify the concept. For that reason, we consider current in it’s macroscopic, seemingly continuous form, and the same goes for water.

Both current and water, as per English language, ‘flow’. Both flowing consist of motion of the constituent particles. The flow of current through a wire could easily be thought of as the flow of water through a pipe. In fact, the low resistance that a connecting wire offers to current can be thought of as the friction between the pipe and the water.

Numerically, current is measured as the amount of charge passing through a cross-section of the conductor per unit time. Based on our analogy, we have current as the amount of water, the volume, that passes through a cross section of the pipe in a unit of time. So, our analogy, with respect to current, is complete.

Potential Difference

A battery produces a direct current when connected to a complete circuit. Actually, what it does is produce a potential difference, and the charges start flowing within the circuit, from the positive terminal to the negative terminal. It is common knowledge that a flow is always from a region of higher potential(im a more general sense of the word) to lower potential. Heat flows from a region of higher temperature to a region of lower temperature. Temperature is the ‘potential’ for heat.

A body released at a height falls down to the ground. Height from the ground is the ‘potential’ in terms of gravity on Earth. Similarly, Voltage is the potential in case of currents. Since our analogy uses water, our potential has to be height. Think of it this way — a battery is a device that tilts our pipe such that one end is higher than the other, with a machine that pumps water from the lower end back to the upper end. Due to the difference in heights, water flows.

For comparison, the potential difference may be equated to the angle of tilting of the pipe from the horizontal. (Also, for the integrity of the analogy, keep the angle less than {\pi\over 2}. It is the difference in angle that matters here, so at times when numerical comparison is required, one may set a value of how many volts a degree of tilt represents.)

Resistance

This is fairly simple one. Resistors are a type of component of the electric circuit that resists the flow of current. In terms of potential difference, what a resistor does is decrease the voltage drop across itself. The current does not pass as freely through a resisor as it does through a wire. In our analogy, a resistor is a part of the pipe whose tilt is in the opposite direction to the tilt caused by the battery. As mentioned above, for all comparative purposes, the resistance offered per degree of tilt is our choice. For our analogy to work, it is better to keep between 0 and {\pi\over 2}. The upward(considering that the battery causes a downward tilt,) tilt makes it difficult for the water to flow over that part. Once it passes through that part, the water experiences the same downward tilt as before.

Note that this analogy works as far as we consider direct currents, and it isn’t as complete as to explain more subtle effects, like magnetism, and working of components like an inductance or a capacitor. But, it does help in creating a simple picture of the very basic phenomena. Once the reader acquires enough experience in the topic, this analogy may be thrown away, or developed upon to fit other concepts. This is actually how theories are made: conjecture, experimentation, and modifications or rejctions, based on experiments.

Series connections

A series connection of components can be pictured exactly how it seems. All components connected one after the other. Consider three resistors connected in series. In our analogy, it is just three upward inclinations, whose tilts depend on the corresponding resistances, one after the other, connected by pipes that have downward inclinations, whose tilt depends on the battery connected.

In this case, the amount of water flowing through all resistors are same, but the voltage drop across each resistor depends on its tilt, or resistance. This is because the current should be the same across every cross-section of the circuit, it has nowhere else to go. On the other hand, the voltage drop is the relative difference of the tilts — downward by the battery and upward by the resistance. It agrees with observation. In a series circuit, current remains the same through out, while the voltage drop varies from component to component.

Parallel connections

Now consider three resistors in parallel connection. Imagine that our pipe branches into three tubes, each connected to one resistor, and then joins back as one before reaching the battery terminal. It is important to note that each of the three branches has the same tilt. Quite obvious, because, considered alone, each of them is connected to the same battery. Therefore, as expected, each branch has the same voltage.

Coming to currents, since the amount of water inside the pipe is always a constant, no water can come into the pipe. So, the three branches are fed by fractions of the amount of water in the main pipe. The values of these fractions are decided by the resistors. Greater the resistance, lower is the chance of water going through it. Nature always finds the easier path, though the tougher path is not entirely forgotten.

In parallel connections, the difference in resistances divides the current, while in series, the same difference divides the voltage.

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