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.
A continuous time periodic signal \( x(t) \) is given by: \[ x(t) = 1 + 2\cos(2\pi t) + 2\cos(4\pi t) + 2\cos(6\pi t) \] If \( T \) is the period of \( x(t) \), then evaluate: \[ \frac{1}{T} \int_0^T |x(t)|^2 \, dt \quad {(round off to the nearest integer).} \]
The Nyquist plot of a strictly stable \( G(s) \), having the numerator polynomial as \( (s - 3) \), encircles the critical point \(-1\) once in the anti-clockwise direction. Which one of the following statements on the closed-loop system shown in the figure is correct?

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?

If A + B means A is the mother of B; A - B means A is the brother of B; A % B means A is the father of B, and A \(\times\) B means A is the sister of B, which of the following shows that P is the maternal uncle of Q?