# Simple circuit analysis question, voltage across an unknown component

Question: Joe was debugging part of an experimental apparatus, probing around with his voltmeter. Part of the apparatus had two obvious resistors in series with an unknown element, as shown in the diagram below:

The unknown element is hard to reach, so Joe put the negative (black) probe of his voltmeter at the interconnection of the two obvious resistors and then put the positive (red) probe at the other end of each resistor, measuring V1=1.4 V and V2=0.8999 V. What is the voltage (in volts) measured across the unknown element V3?

My line of thinking was, since the sum of all the voltages in a loop is zero, that means the following will be true:
$$V_1+V_2+V_3=0,\ \text{or}$$ $$1.4+0.8999+V_3=0$$ From here, we can calculate the value of V3. Which turns out to be -2.2999 volts. The correct answer is 0.5 volts, and I don't know why. If you can, please use simple method like KVL to solve it since using equations without intuition is not what I'm after. Thanks.

• If the negative end of the probe is between the two resistors and doesn't change between measurements, then what is the relation of the measurements' polarities to each other?
– vir
Commented Aug 3 at 0:20

Perhaps it may be easier to see if you select the negative probe as the default $$\0\:\text{V}\$$:

Then just place the voltmeter measurements where they belong (on the + side, because that's what the voltmeter is reporting.)

With the given zero-reference, the upper wire is $$\+1.4\:\text{V}\$$ and the lower wire is $$\+0.8999\: \text{V}\$$. So the unknown device sits between these two, with the difference being the voltage applied across it.

Then you find, working counter-clockwise as shown:

\begin{align*} 0\:\text{V}-V_2+V_1-V_3&=0\:\text{V} \\\\ \therefore V_3&=V_1-V_2 \end{align*}

And this gets you the same result.

The reference directions are opposite so the voltages must subtract. So the unknown must be either +0.5 or -0.5.

• With the polarities given in the diagram, the unknown must be +0.5V.
– vir
Commented Aug 3 at 0:32
• To write KVL you must BEGIN by assigning reference directions. Then go around a closed loop, + to - adds with a + sign and - to plus with a minus sign. (Or the reverse). It's purely mechanical- no thinking or insight required.
– Fred
Commented Aug 3 at 1:30

My line of thinking was, since sum of all the voltages in a loop is zero that means the following will be true:

V1+V2+V3=0

This equation does not agree with the reference directions indicated for the components in the circuit diagram.

On the other hand, the measurements values given, along with the reference directions given on the diagram, are not consistent with the idea that the devices are "obvious resistors".

So there are problems with both the problem statement and your approach to solving it.