What are the filaments inside a bulbs
See Wiki - LED filament for the idea behind these lightbulbs. Quotation: -
The LED filament is composed of a series of LEDs on a transparent
substrate, referred to as Chip-On-Glass (COG). These transparent
substrates are made of glass or sapphire materials. This transparency
allows the emitted light to disperse evenly and uniformly without any
interference. An even coating of phosphor in a silicone resin binder
material converts the blue light generated by the LEDs into a mixture
of red, blue, and green light to create a specified light temperature.
Degradation of silicone binder, and leakage of blue light are design
issues in LED filament lights. Positive benefits of the LED design are
potential higher efficiencies by the use of more LED emitters from
lower driving currents – major benefit of the design is the ease with
which near full 'global' illumination can be obtained from arrays of
filaments.
Picture taken from here
It's difficult to say how many LEDs are involved but if they are 3 volt LEDs and the mains is rectified and smoothed from 230 VAC to 324 V DC then 100 or so of these substrated LEDs might be used and also a current limiting resistor or transistor circuit.
What is the circuit?
It could be as simple as a bridge rectifier, smoothing capacitor and a linear current regulator with all the LEDs in series.
Are there capacitors or resistors involved?
Almost certainly.
