When the current in the circuit used to heat the filament is...

The cutoff wavelength (or minimum wavelength) of the continuous X-ray spectrum is given by:

\lambda_\min = \dfrac{hc}{eV}

where $V$ is the accelerating potential difference between the cathode and the anode.

The current in the filament circuit only controls the temperature of the filament. An increase in filament current increases the number of electrons emitted per second due to thermionic emission, which increases the intensity of the X-rays produced.

However, it does not change the maximum kinetic energy of the electrons striking the target, which depends solely on the accelerating voltage $V$.

Therefore, the cutoff wavelength is independent of the filament current and will remain unchanged.