The power factor of an ordinary electric bulb is

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Examoogle · Accepted Answer

slightly less than unity

Explanation: An ordinary incandescent electric bulb contains a tungsten filament which acts as a resistive load. While it is predominantly resistive, the physical coil structure introduces a very small amount of inductive reactance, causing the power factor to be slightly less than unity (typically 0.95 to 0.99).

Working Principle: The power factor (PF) is defined as the cosine of the phase angle $\phi$ between the supply voltage and current. In an ideal pure resistor, the voltage and current are in phase ($\phi = 0^\circ$), resulting in a power factor of $\cos(0^\circ) = 1$. However, the filament of an electric bulb is wound into a tight coil to increase resistance within a small space, creating a small self-inductance ($L$). This inductance causes a phase lag between voltage and current, making the PF slightly less than unity.

Key Formulas: $PF = \cos(\phi) = \frac{R}{Z}$; $Z = \sqrt{R^2 + X_L^2} = \sqrt{R^2 + (2\pi f L)^2}$

Key Points: An incandescent lamp is primarily a resistive load.; The filament coil acts as a small inductor ($L$).; Inductance causes the current to lag behind the voltage.; The power factor of a purely resistive load is exactly 1 (unity).; Practical bulbs deviate from unity due to inherent self-inductance of the coil.

Advantages: High efficiency of energy conversion to heat and light; Simple operation on AC or DC supplies

Disadvantages: Low luminous efficacy; Short filament life due to high temperature operation

Applications: Domestic lighting; Heating applications; Laboratory resistive load banks

Additional Info: The power factor of an incandescent bulb is often cited in textbooks as unity for ideal purposes, but 'slightly less than unity' is the technically correct answer in engineering examinations when considering the inductive nature of the coiled filament.. Option B (unity) is often considered correct in elementary physics, but is imprecise for electrical engineering contexts.

Answer: D is correct — The filament coil possesses a small amount of self-inductance which causes a slight phase lag in current, resulting in a power factor just below unity.

Exam Tip: Always remember that in electrical machines and components, 'unity' power factor is an ideal state; real-world components almost always have parasitic inductance or capacitance.

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