got water? - A simple circuit for plant watering

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Cristiano Lino Fontana¹, Stefania Lippiello<sup>2

1</sup>Department of Physics and Astronomy “Galileo Galilei”, University of Padova, Italy
²Liceo "Angela Veronese", Montebelluna (TV), Italy

Table of contents

• Introduction
• Measuring the soil humidity
• A reference voltage
• Comparing voltages
• Practical considerations
• Suggested values calculator

Introduction

We introduce here an activity for high school students to get them more acquainted with simple electronics circuits. The aim is to build a simple circuit that lights a LED when a plant needs watering. The only prerequisites are the knowledge of Ohm's law and Kirchhoff's laws.

This work has been published in Physics Education: C.L. Fontana, S. Lippiello and S. Dal Pio, 2019 Phys. Educ. 54 035011 "Combining theory and practice to solve a common problem: a simple circuit for indoor plants watering" DOI:10.1088/1361-6552/ab090d

Physical concept: the soil resistance

Intuitively we know that something wet conducts electricity better than something dry. Therefore we could attach a battery and a light bulb to a pot soil and see the different light intensity. The problem of this approach is that the light would be on only when the plant has just been watered, and not when it needs water. As we want a circuit that can notify us when the plant needs water we will build a different circuit.

Figure 1. Diagram showing the effect of a dry or wet soil in a circuit.

Measuring the soil humidity

Figure 2. Circuit diagram for measuring the soil humidity

Fig. 2 shows the first part of the circuit that we will employ. Let us define the elements:

• \(R_1\) and \(R_2\) are two regular resistors;
• \(\color{#d62728}{R_s}\) is the resistance of the plant soil;
• \(\Delta V_\text{gen}\) is the generator's potential difference;
• \(I\) is the current flowing through the circuit;

and analyze this simple circuit. \(V_\text{A}\) is directly connected to the positive side of the generator and \(V_\text{C}\) to the negative side, therefore the potential difference between the two is equal to \(\Delta V_\text{gen}\): \begin{equation} \Delta V_\text{gen} = V_\text{A} - V_\text{C}. \end{equation} In this circuit the resistors are in series and therefore the equivalent resistor is \begin{equation} R_\text{eq} = R_1 + \color{#d62728}{R_s} + R_2. \end{equation} Remembering Ohm's law, \begin{equation} V = I R, \end{equation} we can calculate the current flowing through the circuit as \begin{equation} I = \frac{\Delta V_\text{gen}}{R_\text{eq}} = \frac{\Delta V_\text{gen}}{R_1 + \color{#d62728}{R_s} + R_2}. \end{equation} Remembering Kirchhoff's loop rule, we can calculate the potential of \(V_\text{B}\) in respect to \(V_\text{C}\). For simplicity we can say that \(V_\text{C} = 0\ \text{V}\) and therefore

• \(\Delta V_\text{AC} = V_\text{A} - V_\text{C} = V_\text{A} = \Delta V_\text{gen}\),
• \(\Delta V_\text{BC} = V_\text{B} - V_\text{C} = V_\text{B} = I R_2\).

Substituting the value for the current \(I\) that we just calculated we get \begin{equation} V_\text{B} = I R_2 = \frac{\Delta V_\text{gen}}{R_\text{eq}} R_2 = \Delta V_\text{gen}\frac{R_2}{R_1 + \color{#d62728}{R_s} + R_2}. \end{equation} According to our daily experience, we know that water conducts electricity well and therefore we can identify two cases

1. Wet soil: there is a lot of water in the soil and then we expect that the soil conducts well, in other words: \(\color{#d62728}{R_s}\) is small.
2. Dry soil: there is no water in the soil and then we expect that the soil conducts badly, in other words: \(\color{#d62728}{R_s}\) is big.

Wet soil: small \(\color{#d62728}{R_s}\)

What happens when we have a wet soil? \(\color{#d62728}{R_s} \approx 0\), therefore we can see what happens to \(V_\text{B}\): \begin{equation} V_\text{B} = \Delta V_\text{gen}\frac{R_2}{R_1 + \color{#d62728}{R_s} + R_2} = \Delta V_\text{gen}\frac{R_2}{R_1 + R_2}. \end{equation} So \(V_\text{B}\) becomes an intermediate value between \(0\ \text{V}\) and \(\Delta V_\text{gen}\), depending on the values of \(R_1\) and \(R_2\).

Dry soil: big \(\color{#d62728}{R_s}\)

In this case we have that \(\color{#d62728}{R_s}\) is big and therefore: \begin{equation} V_\text{B} \rightarrow 0\ \text{V} \end{equation} in other words \(V_\text{B}\) becomes very small. We see that we have found a way to generate a variable potential that is related to the soil humidity.

A reference voltage

For having a healthy plant we can decide what is the minimum level of humidity that we want to keep in the soil. How do we create a reference voltage that can tell us if \(V_\text{B}\) is too high or too low? We can use a potentiometer that can give an adjustable voltage.

Figure 3. Circuit diagram with a potentiometer generating a reference voltage \(V_\text{ref}\).

Fig. 3 shows a circuit in which a potentiometer is used to define a reference voltage \(V_\text{ref}\). Potentiometers have a sliding contact that can select a voltage that goes from the minimum voltage \(V_\text{C}\) to the maximum voltage \(V_\text{A}\).

Comparing voltages

Now that we have a reference voltage \(V_\text{ref}\) and a voltage that we want to compare it to \(V_\text{B}\), we need an instrument that can tell us if the unknown voltage is less or more than the reference. For this task we can employ an operational amplifier, also commonly called op-amp. Op-amps are complicated devices, but do not panic and bear with me! We can use an op-amp as comparator in a extremely simple configuration.

Figure 4. Circuit diagram of an operational amplifier used as a comparator.

Fig. 4 shows the circuit diagram of an op-amp. It is an active device and therefore it needs to be powered by the generator. The power supply need is represented by the two vertical lines, one is connected to the generator voltage and the other to the zero voltage of the circuit. This device has two inputs \(V_+\) and \(V_-\) and one output \(V_\text{out}\). When an op-amp is used as a comparator its behavior can be described by the following \begin{align} \text{if} \quad V_+ - V_- \gt 0 & \Rightarrow \ V_\text{out} = \Delta V_\text{gen} \\ \text{if} \quad V_+ - V_- \lt 0 & \Rightarrow \ V_\text{out} = 0\ \text{V} \end{align} Therefore if we connect \(V_\text{ref}\) to the \(V_+\) input and \(V_\text{B}\) to the \(V_-\) input, we can compare the two voltages and determine which one is greater. What if we connect a LED to the output of the comparator? Let us analyze the two cases:

1. Wet soil \(\Rightarrow\) soil has a small resistance \(\Rightarrow\) \(\color{#d62728}{R_s}\) is small \(\Rightarrow\) \(V_\text{B}\) is high \(\Rightarrow\) \(V_\text{ref} - V_\text{B} \lt 0\) \(\Rightarrow\) \(V_\text{out} = 0\ \text{V}\) \(\Rightarrow\) LED is OFF.
2. Dry soil \(\Rightarrow\) soil has a big resistance \(\Rightarrow\) \(\color{#d62728}{R_s}\) is big \(\Rightarrow\) \(V_\text{B}\) is low \(\Rightarrow\) \(V_\text{ref} - V_\text{B} \gt 0\) \(\Rightarrow\) \(V_\text{out} = \Delta V_\text{gen}\) \(\Rightarrow\) LED is ON.

Figure 5. Circuit diagram of the complete circuit.

Fig. 5 shows the complete circuit diagram. On the output we connected a LED in series with a resistor \(R_\text{L}\), that is necessary for the good functioning of the LED.

Practical considerations

Suitable values for \(R_1\) and \(R_2\) can be calculated with the calculator below. The calculator requires a measurement of the soil resistance. We suggest to have the soil with a intermediate humidity for this measurement. In order to measure the soil resistance, two electrodes should be inserted in the soil. The electrodes can be simple pieces of iron wire as long ad the pot height. The rationale for having two resistors around \(\color{#d62728}{R_s}\) is to clamp the possible values of \(V_\text{B}\), in order to be sure to be always able to set a value of \(V_\text{ref}\) that is above or below.

The potentiometer can be of any kind of potentiometer, total resistances of \(10\ \text{kΩ}\) or \(100\ \text{kΩ}\) are good values. The op-amp can be a LM358 that is very easily found and it is cheap. The LED can be a regular red LED.

A set of three or four AA batteries in series can be used as a generator. With this option \(\Delta V_\text{gen}\) will be either \(4.5\ \text{V}\) or \(6\ \text{V}\), that work well with the LM358. A breadboard is a good option as the circuit support.

Suggested values calculator

Here we suggest reasonable values fot the resistors \(R_1\), \(R_2\) and \(R_\text{L}\), given the generator voltage and a measured soil resistance.

Suggested values calculator

Generator voltage \(V_\text{gen}\) [\(\text{V}\)]:

Measured soil resistance \(\color{#d62728}{R_s}\) [\(\text{Ω}\)]:

Suggested values:

• \(R_1\): Ω
• \(R_2\): Ω
• \(R_L\): Ω