Voltage through resistor connected to tesla coil
DC gas-discharge voltage (post-breakdown spark-gap voltage) isn't simple, and depends on the spark-length, value of current, the type of metals, the time-length of the spark, the temperature of the metal surface, the gas mixture, initial gas temperature, dust contamination, etc.  Spark-plasma is a fairly good conductor.  Roughly expect the voltage along the spark to be somewhere between ten and a few hundred.

So, the voltage across the resistor will briefly be about 40KV, minus the small voltage which appears across the spark.  VERY briefly.

After some nanoseconds, the voltage of the Tesla Coil will have collapsed.  Its stored energy was discharged.  (A Tesla Coil's secondary coil is something like a capacitor, also something like an energy-storage inductor.)  The energy which had been stored in the Tesla Coil will mostly end up inside the spark-plasma, with some being deposited into your 1-ohm resistor.  Use a much large resistor value if you want the energy to mostly end up inside the resistor.

Find books on DC gas-discharge at one atmosphere.  It's an ancient topic, so not much exists online.   Here's the V-I curve for a fairly long discharge in a neon tube:


https://www.plasma-universe.com/File:Glow_D.jpg