AIPMT PRELIMS 2004 Physics Potential Difference MCQ Question

To solve the question, we need to find the potential difference between two points on a wire that has a uniform resistance. Let's break down the problem step by step.

Given Data:

• Total voltage of the battery, $V = 6 \, \text{V}$
• Length of the wire, $L = 3 \, \text{m}$
• Total resistance of the wire, $R = 100 \, \Omega$
• Distance between the two points on the wire, $d = 50 \, \text{cm} = 0.5 \, \text{m}$

Step 1: Calculate the Current in the Circuit

First, we need to calculate the current flowing through the wire when it is connected to the battery. According to Ohm's Law, the relationship between voltage ($V$), current ($I$), and resistance ($R$) is given by:

$$I = \frac{V}{R}$$

Substituting the values, we get:

$$I = \frac{6 \, \text{V}}{100 \, \Omega} = 0.06 \, \text{A}$$

Step 2: Calculate the Resistance per Meter of the Wire

Next, we need to determine the resistance per unit length of the wire. The total resistance is given as $100 \, \Omega$ for a length of $3 \, \text{m}$. Therefore, the resistance per meter ($R_{\text{per meter}}$) is:

$$R_{\text{per meter}} = \frac{R}{L} = \frac{100 \, \Omega}{3 \, \text{m}} \approx 33.33 \, \Omega/\text{m}$$

Step 3: Calculate the Resistance for 0.5 m

Now, we find the resistance of the segment of the wire that is $0.5 \, \text{m}$ long:

$$R_{0.5 \, \text{m}} = R_{\text{per meter}} \times 0.5 \, \text{m} = 33.33 \, \Omega/\text{m} \times 0.5 \, \text{m} \approx 16.67 \, \Omega$$

Step 4: Calculate the Potential Difference Across 0.5 m

The potential difference ($V_d$) across this segment of wire can be calculated again using Ohm's Law, but we will use the current we found earlier:

$$V_d = I \times R_{0.5 \, \text{m}}$$

Substituting the values:

$$V_d = 0.06 \, \text{A} \times 16.67 \, \Omega \approx 1 \, \text{V}$$

Conclusion

Thus, the potential difference between the two points separated by $0.5 \, \text{m}$ on the wire is approximately $1 \, \text{V}$. Therefore, the correct answer is:

B) 1 V

Clarification of Other Options:

• Option A (3 V): This would imply a much larger distance on the wire or a higher current, which is not the case here given the total voltage and resistance.
• Option C (1.5 V): This value is not consistent with the calculated potential difference based on the resistance and current.
• Option D (2 V): Similar to option C, this value does not align with our calculations based on the resistance for the given length.

In summary, the potential difference of $1 \, \text{V}$ between the two points on the wire is derived from the calculations based on Ohm's Law, confirming that option B is indeed the correct answer.