Concept:
The power factor measures how effectively electrical power is converted into useful work output. It is defined as the cosine of the phase angle (\(\phi\)) between the voltage and current.
Step 1: Understanding the Question:
The question asks for the power factor in an Alternating Current (AC) circuit containing only a pure resistor.
Step 2: Key Formula or Approach:
Power Factor = \(\cos \phi\).
In AC circuits:
- Resistor: Voltage and current are in phase.
- Inductor: Current lags voltage by \(90^\circ\).
- Capacitor: Current leads voltage by \(90^\circ\).
Step 3: Detailed Solution:
1. For a purely resistive circuit, the phase difference \(\phi = 0^\circ\).
2. Power factor = \(\cos(0^\circ)\).
3. Since \(\cos(0^\circ) = 1\), the power factor is unity.
This means that in a pure resistor, all the supplied electrical energy is dissipated as heat (real power).
Step 4: Final Answer:
The power factor of a pure resistor is 1.