Question

What is the power factor of an AC circuit containing only a pure resistor?

• A. \(0\)
• B. \(0.5\)
• C. \(1\)
• D. \(-1\)

Hint:

Power factor values for basic AC circuits:
• Pure resistor → \(1\)
• Pure inductor → \(0\) (lagging)
• Pure capacitor → \(0\) (leading) A unity power factor represents maximum efficiency of power usage.

Answer 1

The Correct Option is C

Concept: The power factor in an AC circuit is defined as \[ \text{Power Factor} = \cos \phi \] where \( \phi \) is the phase difference between voltage and current. The value of the power factor indicates how effectively electrical power is converted into useful work.

Step 1: Understand the behavior of a pure resistor in AC. In a circuit containing only a pure resistor:
• The current and voltage reach their maximum and minimum values at the same time.
• There is no phase difference between voltage and current. Thus, \[ \phi = 0^\circ \]

Step 2: Calculate the power factor. \[ \text{Power Factor} = \cos 0^\circ \] \[ = 1 \]

Step 3: Interpretation. A power factor of \(1\) means that all the supplied electrical power is effectively used for useful work, and no power is wasted due to reactive components. \[ \boxed{1} \]