Which of the following bulbs will have the least resistance ?

Question

Examoogle · Accepted Answer

$115 	ext{ V}, 100 	ext{ W}$

Explanation: The resistance of an electric bulb is determined by its rated power and voltage, calculated using the relationship $R = \frac{V^2}{P}$. A bulb with higher power and lower voltage rating will yield the smallest numerical value for resistance.

Working Principle: The resistance of a filament is a constant characteristic derived from its design parameters: voltage ($V$) and power ($P$). Since $P = \frac{V^2}{R}$, rearranging gives $R = \frac{V^2}{P}$. In this comparison, $115V$ reduces the numerator significantly compared to $220V$, and the $100W$ rating maximizes the denominator, leading to the minimum resistance value.

Key Formulas: $R = \frac{V^2}{P}$ — Resistance in terms of rated voltage and power

Key Points: Resistance is inversely proportional to power for a fixed voltage.; Resistance is directly proportional to the square of the rated voltage.; The combination of low voltage and high power results in the lowest resistance.

Advantages: High power bulbs have thicker filaments to handle higher currents.; Lower voltage ratings result in shorter filament lengths for a given power, reducing resistance.

Disadvantages: Filaments with low resistance are more susceptible to high inrush currents upon switching.; Lower resistance elements require specific voltage sources to prevent burnout.

Applications: Incandescent lighting design; Heater element manufacturing; High-current surge protection devices

Additional Info: Option A: $R = 806.67 \Omega$. Option B: $R = 484 \Omega$. Option C: $R = 220.41 \Omega$. Option D: $R = 132.25 \Omega$ (Minimum)

Answer: D is correct — The bulb with $115 	ext{ V}$ and $100 	ext{ W}$ yields the lowest resistance because resistance is proportional to the square of voltage and inversely proportional to power.

Exam Tip: Always remember the $R = \frac{V^2}{P}$ relationship for bulb problems; it is a common trap in exams where students mistakenly assume higher wattage always implies lower resistance regardless of voltage.

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