Final answer:
Increasing the resistance in a lightbulb's circuit lowers the power dissipation, which in turn reduces the filament temperature and causes the emitted light spectrum to shift toward redder hues.
Step-by-step explanation:
When a lightbulb is wired to a variable resistor and the resistance of the circuit is increased, the current through the lightbulb decreases due to Ohm's law, resulting in a lower power dissipation across the bulb.
Consequently, the filament temperature of the bulb drops and the color spectrum emitted shifts toward longer wavelengths. According to the relationship v = fλ (where v is the speed of light, f is the frequency, and λ is the wavelength), since the speed of light is constant, a decrease in frequency implies an increase in wavelength. This shift is observed as the color of the light moving from white to a redder hue, confirming option d as the correct answer. Referencing Figure 1.29, as the temperature decreases, the intensity of radiation decreases and the spectrum shifts up towards the red part of the spectrum.