AIPMT PRELIMS 2004 Physics Resistance and Power MCQ Question

To solve the problem, we need to understand the relationship between power, voltage, and resistance in electrical devices, particularly light bulbs. The power consumed by an electrical device can be expressed using the formula:

$$P = \frac{V^2}{R}$$

where:

• $P$ is the power (in watts),
• $V$ is the voltage (in volts),
• $R$ is the resistance (in ohms).

Step 1: Calculate the Resistance of the Bulb in India

In India, the power rating of the bulb is given as 60 W, and the supply voltage is 220 V. We can rearrange the power formula to find the resistance $R$:

$$R = \frac{V^2}{P}$$

Substituting the values for the Indian bulb:

$$R = \frac{(220)^2}{60}$$

Calculating $R$:

$$R = \frac{48400}{60} = 806.67 \, \Omega \quad \text{(approximately)}$$

Step 2: Calculate the Resistance of the Bulb in the USA

Now, we need to find the resistance of a 60 W bulb when supplied with a voltage of 110 V in the USA. Using the same power formula:

$$R' = \frac{V'^2}{P}$$

where $V' = 110 \, V$ (the voltage in the USA). So we substitute the values:

$$R' = \frac{(110)^2}{60}$$

Calculating $R'$:

$$R' = \frac{12100}{60} = 201.67 \, \Omega \quad \text{(approximately)}$$

Step 3: Relating the Resistances

Now, we can relate the resistance of the bulb in the USA to that in India. We can express $R'$ in terms of $R$:

From our calculations:

• Resistance in India: $R = \frac{48400}{60}$
• Resistance in the USA: $R' = \frac{12100}{60}$

To find the relationship between $R'$ and $R$:

$$R' = \frac{12100}{48400} \times R = \frac{1}{4} R$$

This shows that the resistance of the bulb in the USA is one-fourth the resistance of the bulb in India.

Conclusion

Thus, if the resistance of a 60 W bulb for use in India is $R$, then the resistance of a 60 W bulb for use in the USA will be:

$$R' = \frac{R}{4}$$

Final Answer

The correct answer is B) R/4.

Clarification of Other Options

• A) 2R: This implies that the resistance in the USA would be double that in India, which contradicts the relationship we derived.
• C) R/2: This suggests that the resistance in the USA is half that of India, which is also incorrect based on our calculation.
• D) R: This option indicates that the resistances are equal, which does not hold true since we have established a different relationship.

Hence, the only correct answer is B) R/4.