# How can there be voltage across resistors in series when circuit is open?

If you have a circuit containing 5 resistors, and one of them gets damaged such that current can't flow through it, I assumed no current would flow anywhere throughout the circuit, and that the voltage across each resistor would therefore also be zero. However, I watched a video where a string of Christmas lights (all in series) were failing to light up because of one broken bulb, and the user could detect voltage across each of the bulbs except the broken one.

Here is the video. Just watch from 17:15 to 18:10 to see the user find voltage in one of the bulbs (he previously found voltage in all the 'upstream' bulbs) and find no voltage in the next 'downstream' bulb.

What I Want To Know: Why is it not the case that having one resistor (light bulb in this case) break does not cause the voltage across all the other resistors in series to be zero?

• Could we see this video? Was the voltage actually across the bulbs? Commented Dec 15, 2020 at 5:06
• @SomeoneSomewhereSupportsMonica I've edited the original question ^^ thanks Commented Dec 15, 2020 at 5:13
• If by 'break' you mean the resistance becoming a short, then he mentions in 6:00 onwards that this would eventually be the reason of all the bulbs in the row to burn due to higher voltage drop across the rest of the bulbs in the series of 50 But if you mean it becoming an open circuit, then indeed the main question is how do the working ones before and after the bad one have any voltage at all to be measured. N0m4d got it.
– Geo
Commented Dec 15, 2020 at 5:39
• he is not measuring voltage across light bulbs ... the result would be the same if he separated the wires of a power cord that is plugged into a power outlet Commented Dec 15, 2020 at 5:50
• Indeed, that the voltage being measured is that of the hot and not across the bulb was exactly the issue explained at your question of yesterday: electronics.stackexchange.com/questions/537174/… Commented Dec 15, 2020 at 6:46

Why is it not the case that having one resistor (light bulb in this case) break does not cause the voltage across all the other resistors in series to be zero?

It does. There is practically no voltage across the other bulbs. However there is a voltage coming from the mains, which goes through the bulbs and appears at the last one before the disconnection.

The question is, how was he able to detect this voltage without connecting anything to it? The answer is that his detector is able to sense a very small current caused by nearby voltage changes, due to the tiny capacitance between the wire and the detector.

The circuit looks like this:-

simulate this circuit – Schematic created using CircuitLab

With a mains voltage of 120 V the voltage at the wire is tracing a sine wave going from ~ -170 V to +170 V. This induces a current in nearby metallic objects because the electrons in the wire produce an electric field which repels other electrons, while positive charge attracts them. As the field changes polarity the electrons in the nearby metal are alternately pushed and pulled, creating a tiny current and voltage in time with the AC mains.

As distance increases the electric field and induced current get smaller, but with 170 V at the source a useful voltage still can be detected from a distance of a few cm if the sensor has a very high input impedance. However it will not be able to accurately measure the voltage at the wire, because the loss varies with distance and amount of 'plate' area between the wire and detector, as well as how well the sensor is 'grounded' through the person holding it.

• Hi Bruce, thanks for your reply. Two main clarifying questions: 1) Re "There is practically no voltage across the other bulbs. However there is a voltage coming from the mains, which goes through the bulbs": How are those two different? I assumed there was zero voltage anywhere in the circuit; could you explain more what this "voltage coming from the mains" is? And 2) Re "a tiny current and voltage": I understand that an AC current induces current/voltage in nearby metal objects, but there aren't any. Does it just induce voltage in the air/surroundings, and that's what the detector is sensing? Commented Dec 15, 2020 at 15:40
• Current creates a magnetic field, voltage creates an electric field. Both types of field influence electrons from a distance. Current is the movement of electrons, and voltage is their electric charge. hyperphysics.phy-astr.gsu.edu/hbase/Forces/funfor.html#c3 Commented Dec 15, 2020 at 16:32