Electrostatics
ID: #1047 | Difficulty: medium
AI Quick Answer:
The correct option for this defence exam question is (A) which is 0.344 \Omega. Detailed proof and explanation are supplied below.
A copper wire has a resistivity of 1.72 \times 10^{-8} \Omega\cdot m, length of 10 m, and a cross-sectional area of 0.5 mm². What is its electrical resistance?
Key Takeaways for NDA & CDS Candidates
- Ensure you recall the standard formulas for Electrostatics during UPSC exam preparation.
- Eliminating obviously incorrect choices based on dimensional analysis or limits saves valuable seconds.
- Expert tip: Written defence mock tests should be practiced weekly with strict negative marking rules.
Correct Answer: (A)
0.344 \Omega
Step-by-Step Explanation
The resistance R of a conductor is given by:
R = \rho \frac{L}{A}
Where:
\rho = 1.72 \times 10^{-8} \Omega\cdot m (Resistivity)
L = 10 m (Length)
A = 0.5 mm² = 0.5 \times 10^{-6} m² (Cross-sectional Area)
Substituting the values:
R = (1.72 \times 10^{-8}) \times \frac{10}{0.5 \times 10^{-6}} = 0.344 \Omega.
R = \rho \frac{L}{A}
Where:
\rho = 1.72 \times 10^{-8} \Omega\cdot m (Resistivity)
L = 10 m (Length)
A = 0.5 mm² = 0.5 \times 10^{-6} m² (Cross-sectional Area)
Substituting the values:
R = (1.72 \times 10^{-8}) \times \frac{10}{0.5 \times 10^{-6}} = 0.344 \Omega.
| Question Metadata Summary | |
|---|---|
| Exam Category | UPSC NDA / CDS / AFCAT / Agniveer |
| Subject Unit | NDA Physics Questions |
| Sub-topic / Module | Electrostatics |
| Correct Option | Option (A) |
| Target Year | UPSC Defence Exams 2026 |