The power factor is a measure of how effectively electrical power is being utilized in a circuit. It is the ratio of the actual power (real power) to the apparent power (product of voltage and current). A power factor of 1 indicates maximum power utilization, while a power factor close to 0 indicates poor power utilization.

In order to determine in which case the power factor will be negligible, let's analyze the given options:

A) Inductance and resistance both high:
- When both inductance and resistance are high, it implies that the circuit has significant reactance and resistance.
- In this case, the power factor will not be negligible because even though the inductance causes a phase shift between the voltage and current, the resistance will contribute to the real power, resulting in a non-negligible power factor.

B) Inductance and resistance both low:
- When both inductance and resistance are low, it implies that the circuit has minimal reactance and resistance.
- In this case, the power factor will not be negligible because without significant reactance, the phase shift between the voltage and current will be minimal, resulting in a non-negligible power factor.

C) Low resistance and high inductance:
- When the resistance is low and the inductance is high, it implies that the circuit has significant reactance but minimal resistance.
- In this case, the power factor can be negligible because the inductance will cause a large phase shift between the voltage and current, resulting in a lower power factor.

D) High resistance and low inductance:
- When the resistance is high and the inductance is low, it implies that the circuit has minimal reactance but significant resistance.
- In this case, the power factor will not be negligible because without significant reactance, the phase shift between the voltage and current will be minimal, resulting in a non-negligible power factor.

Therefore, the correct answer is C) low resistance and high inductance, where the power factor can be negligible.