Lets pretend a LED has equivalent resistance R and needs I amps current to light up properly at V volts. If you put two in series, you have 2R and you need 2V, ie double the voltage for them both to light up. Ohm's law V=IR, so we have I=2V/2R=I again. Same thing happens if you have five in series etc, it's still only I amps current flowing through the string of LEDs.

This is for continuous steady state operation. Ignores initial starting transients, where different bulbs may draw currents to fire up. If one bulb looks like a much lower resistance to the others, it will have fewer volts across it, which means there are more volts distributed across the others (Kirchhoff's Law) maybe causing them to blow.

One downside to LEDs: they look weird in videos.

It's faint since it's bright out, but take a look at this video and you can see it on the engine on the right.
https://youtu.be/lwN6FlPyjSQ?t=733

But you wouldn’t have 2V unless you’re doubling the voltage when you add the second bulb in series. To keep it simple, you add the resistances of the components in series and divide that into your voltage available. That gives you the total current of the circuit. You would, in effect, be asking an LED bulb to be able to handle that current, would you not? I don’t imagine that LEDs bulbs, which require an internal regulator to drop the voltage down to the individual diodes voltage rating, are as robust as an incandescent bulb due to the physical size of the internal components that you’re asking to pass the current. Like the way a fuse works, if you exceed those tiny components current rating, something is gonna pop.

Or maybe I’ve forgotten more than I thought.

A typical frame rate for video is 30fps. If that is close to a multiple of the LED flash rate, you’ll get a weird strobing effect. Take a video of your car’s LED brake lights and you’ll get the same effect.

Assume a LED takes a minimum of V volts to light up. If you don't double the voltage across two such LEDs in series, they don't light up!

Just having a car with LED brake lights go past me at night-time can make the strobe effect appear in my peripheral vision.

No because the current for the whole circuit is the same as the current for each component. Also LEDs only look weird if you're using a switch mode power supply (which most of them are) if you're just using Straight DC the lights on flicker at all.

AH-HA! I was correct! I have forgotten more than I thought. Pulled out my ancient handbook. Please disregard my previous assumptions on series current….

However, I think my thought of stepping down and regulating the voltage and wiring bulbs in parallel would help prevent blowing out a hole string of lamps due to an arc on the trolley pole. You wouldn’t have to consider voltage drop down a series string, either. Dunno, could be wrong there, too. Or a solution looking for a problem.

Does the same strobe effect happen when making videos inside a house with LED bulbs? If that's the case, manufacturers are going to have to come up with a solution, such as a super capacitor in the power supply, to keep the LED's lit. Nobody wants the psychedelic effect in their kids birthday videos.

Yes and no. It depends how the lights are placed and what circuitry they use. From my experience I don't see any flickering in a room lit by LEDs but if I put the camera right up to the light bulb then all hell breaks loose. They sell "flicker free LEDs" but your mileage may vary. The problem is LEDs are instant on and off with an incandescent bulb when the power drops there's still residual heat in the filament to keep it glowing that was a slow motion camera you will see it dim and brighten. The popular way a lot of these bulbs are driven is with a switch mode power supply which converts the current to high frequency AC and then drops or raises it. And with Cutthroat competition and China they try to use as few components as humanly possible. So what the human eye can't normally see is ignored. Although not as efficient is a switch mode power supply you could just use a voltage regulator IC what's in a capacitor is this moves the output to get a smooth light output.

Please be aware that LED bulbs incorporate an electronic circuit to convert the power applied into the current and voltage necessary to drive the LEDs themselves. Most will have many individual LED devices such as the 'Edison' type bulbs with strings of LEDs simulating the filament of an incandescent bulb. Others have fewer but larger LEDs to generate brighter light such as floodlights and headlights.

DC input devices may flicker at rates in the many thousands of Hz (cycles per second) so they should not affect cameras. AC devices on 60 Hz power will likely flicker at a 120 Hz rate. A dimming control can have a large affect on the flicker for either AC or DC.

They are NOT like incandescent bulbs in how they draw power from the source and they can't be treated as a resistor. A 5 watt LED bulb will draw 5 watts regardless of whether the input is 50 volts or 100 volts.

As far a flicker being detected with LED lights, it's completely dependent on that particular light.
My quick test for flicker is to wave my hand rapidly back and fourth under the suspected light. If you see any strobe effect the ballast is cheap or there is none, as in LED Christmas lights.
Google "film production LED lighting" and you will see hundreds of lights that do not flicker at all, and come in a wide range of color temperatures. TV engineering used to be my day job. I can tell you that LED lights can do everything an incandescent can do without the massive power consumption and heat. You just have to pay the price for the better stuff.
Getting back to led bulbs, most now have a high frequency (50 to 300 KHZ) ballast like the electronic florescent lights and CFLs do.
If they still flicker is because that little AC/DC to DC converter (ballast) was not filtered sufficiently.
As far as hooking them in series, I would not go there. May be something like hooking ten 12 volt motors in series to a 120 volt circuit to see what happens.

Yes, that last sentence is the important one! LEDs do not have a linear V-I curve. They want to be driven at a specific current, not a specific voltage. Typical forward voltage drop is about 2V. If you use a constant voltage supply and apply say 2.1V, the result isn't a 5% increase in current and brightness, it might be a 10-fold increase, in other words, destroyed!

So all LEDs require some means of keeping the current more or less constant. The dumbest way is to put a big dropping resistor in front of it. But in those screw-in replacement LED bulbs, you have an electronic power supply in the bottom. It is set for a specific current, which is controlled by closed loop feedback. For dimmable LEDs, the input voltage is sensed and this resets the setpoint on the drive current, within the limts of the device of course.

There are a number of different circuit designs. You can simply PWM the 120VAC input, controlling the duty cycle under closed loop control to achieve the current. Those are going to be very flickery. In the better design, you'll have an input bridge recitifer, a small capacitor to create a DC bus, and then a buck type converter with an inductor and some kind of switching element like an IGBT, again controlling the switching duty cycle to regulate the current. Unless you also have a good smoothing capacitor at the output leading to the LED or LED string, there will be flicker at the switching frequency. This might be on the order of 100kHz, which would appear to be way to fast to be caught by a video camera. But if you have several of these LEDs, you can get some odd beat frequency effects and still get flickering. If the driver circuitry is high quality, then it is filtered and it is delivering nearly pure DC, so the LED never goes off and there is no flicker. Capacitors and inductors are bulky components and so guess what often gets sacrificed in cheap consumer grade LED lights?

You certainly could make an LED bulb which responds in the same way as an incandescent, including the soft fade, and the color temperature shift with brightness. Maybe someone already does, actually. But again, in a string-of-5 circuit, I wouldn't trust them.

One way I found the led flicker useful is watching one of those old 33/45/78 strobe disks to set the speed of my turntable. A pair of back-to-back leds on 12VAC provides the brightest light I've ever seen for this purpose, miles ahead of using incandescent or neon bulbs.

ObRailwayContent: I was doing this to digitize a few steam train records I have that have never been released on CD.