Yes, 3kV is too low to power a Tesla coil.
A marx generator will get you the voltage, but that's only half the story of a good spark display, you need power to keep the arc channel hot and conducting, and to sound loud.
There's a more complicated but better way to use your meager 3kV transformer.
First, rectify your 3kV AC, which is about 4kV peak, ...
Danger Will Rogers.... This is a higher power grid powered arc. kW~
A Marx generator has higher impedance than the Tesla Generator, so it multiples by Cap chains, rather than transformer turns ratio and flyback inductance and extremely long ceramic bushings of low capacitance.
Chances are the part, if it actually is a capacitor and actually measures anything like 10uF with no bias, will be more like 0.1 or 0.5uF with 100V across it, assuming it doesn't fail short. Note that it could actually meet the claims - 10uF and 100V, just not at the same time.
The voltage limit on many ceramic caps is determined by the capacitance ...
Here is the X7R availability table from AVX:
The highest capacitance for 0805 100V is 0.47uF; 10uF 100V is not available even in a 1206 package (I am willing to concede that the next capacitance value may be available in X5R).
Personally I would give this one a miss; AVX is one of the best sources out there and they don't make anything even close.
Digikey sell Murata 0805 50V 10 uF X5R for 18.8 cents in 100s.
Digikey do not sell 100V 0805 10 uF ceramic capacitors, at all.
LCSC, an as reputable as they come high volume major Chinese distributor (located in Shenzhen) also do not sell 100V, 0805, 10 uF ceramic capacitors, at all.
For commodity items (and much else) LCSC pricing usually (not always)...
0805 10uF 100V ceramic = scam , The dielectric constant is not high enough
For ceramic with very thin , many layers you can achieve 10uF in small area but not 100V. You can achieve nF 10kV in 1 layer , but not 10uF at this voltage and size.
The product of these 3 parameters : size, capacity and voltage is not achievable in ceramic.
Since capacitors ...
Figure 1. An old-style 20 kΩ/volt multimeter.
These moving coil multimeters mechanism read full-scale at a very low current. We can calculate what this current is by looking at the Ω/V figure for a particular range.
The most sensitive is 2.5 V and the meter's impedance on this range would be 2.5 × 20k = 50 kΩ.
The current that ...
The 10 ohm resistor is simple acting as a current to voltage converter since it is in series with the load. By Ohm's law, the voltage across the resistor in volts is simply 10 times the current through the resistor in amperes. However, the conversion factor is such that the current in milliamperes will be 1/10 the voltage in millivolts since the value of the ...
Yes, it will probably work*, and if the resistors R1 and R2 have high enough value to limit current to a safe value, the opamp will be protected.
However the common mode rejection of this type of difference amplifier depends on accurate matching between resistors. If you want decent CMRR it is quite likely that will require precision resistors which will ...
Using an op-amp in the feedback can work.
It has two drawbacks though.
1) The output voltage will vary non-linearly with the value of R4 (the variable resistor). This means that your adjustment resolution will vary across the range of output voltages.
2) Also you do need to factor in the bandwidth of the op-amp because it becomes part of the feedback path....
Yes and no -- you've identified the biggest potential problem. Typical "general purpose" op-amps are generally fast enough for today's "general purpose" switchers; I'm assuming that your loop will be particularly slow based on the voltage and the UC3843. Basically the bandwidth should be at least ten times the anticipated loop bandwidth of the supply.