(B), since the 3.2K (which is carrying 0.0028A) came
from the 1.2K and 2K in series, both of these will also
Now, here’s where we apply our knowledge of
the voltage divider from earlier. Since 0.0028A is
flowing through the 1.2K, it drops the voltage of the
current by (using Ohm’s Law) V = 0.0028 x 1200 =
3.38V. However, the 1.2K — with the 3.38V drop
across it — came from the 2K and 3K in parallel in
Figure 7 (A). Thus, there’s a 3.38V drop across both
the 3K and the 2K.
Lastly (bear with me), since the 3K came from the
2K and 1K in series (from Figure 6), the 2K and 1K in
Figure 6 must have 3.38V across them as well. Finally,
here’s the clue to what voltage we’ll get from our tree
water level sensor if both wires (a) and (b) are
submerged: Having 3.38V across the 2K and 1K will
mean a current of I = 3.38/3000Ω = 0.0011A will flow
through them. Now looking carefully, you’ll see the
top of the 2K resistor is at 9V and the bottom is where
our voltmeter is connected. Hence, our voltmeter is
measuring the drop (from 9V) in voltage across the
2K, which will be 9V - 0.0011 x 2000 = 6.74V. Thus,
the voltmeter will read 6.74V when the water covers
wires (a) and (b).
All told, you can see where this is going. We get
4.5V when just wire (a) is submerged. Now, we’re
getting 6.76V when the water is deeper and wires (a)
and (b) are submerged. We won’t trouble you with the
calculations to figure out the voltage when (a), (b),
and (c) are submerged. (Wasn’t doing just (a) and (b)
bad enough?) Suffice to say, it’ll be a higher voltage.
While checking all of this work using Falstad’s
circuit simulator ( www.falstad.com/circuit), I found
that the circuit outputs 7.88V when all three depth
wires are submerged. So, we have it then: a circuit
that will output a voltage proportional to the water
depth in our reservoir. The deeper the water, the
higher the output voltage.
Let’s build it now and see what we get.
There is really nothing critical about the wiring or
construction for this project. I started by wiring the
tree holder as shown in Figure 8 using 22 gauge
hookup wire (I drilled some small holes near the top
rim to hold the wires). In this figure, you can see the
three depth wires going from left to right. My positive
9V lead is the rightmost one. Be sure to strip about
1/8” of insulation off of each wire.
Next, I breadboarded the R-2R circuit as shown
in Figure 9. I only had 2.2K resistors in my parts bin,
so my ladder is made from 1K and 2.2K resistors. I
used a 9V battery clip to connect the battery to my
November 2015 29
■ FIGURE 8. Placement of the positive 9V lead (rightmost)
and three depth wires in a standard tree stand.
■ FIGURE 9.
The yellow wire
with the blue
tape is the 9V
The red and
black wires are
from the 9V
The two blue
■ FIGURE 10. Final assembly of a circuit that will output a
voltage proportional to the depth of the water in the