Step 1: Understanding Power Factor The power factor of an electrical load is defined as: \[ \text{Power Factor} = \cos \theta = \frac{\text{Real Power}}{\text{Apparent Power}} \]
Step 2: Power Factor of Filament Lamps
- Filament lamps (incandescent lamps) consist of a resistive heating element (usually tungsten).
- In a purely resistive circuit, voltage and current are in phase, leading to a unity power factor (\( \cos \theta = 1 \)).
Step 3: Evaluating options:
- (A) Incorrect: A lagging power factor is associated with inductive loads (motors, transformers).
- (B) Incorrect: A leading power factor is associated with capacitive loads.
- (C) Incorrect: A zero power factor is observed in circuits dominated by pure reactance (inductors or capacitors).
- (D) Correct: Filament lamps have a unity power factor as they behave like a pure resistive load.
Let \( G(s) = \frac{1}{(s+1)(s+2)} \). Then the closed-loop system shown in the figure below is:
The open-loop transfer function of the system shown in the figure is: \[ G(s) = \frac{K s (s + 2)}{(s + 5)(s + 7)} \] For \( K \geq 0 \), which of the following real axis point(s) is/are on the root locus?