A rectangular parallelopiped is measured as 1 cm × 1 cm × 100 cm. If its specific resistance is 3 × 10⁻⁷ Ω m, then the resistance between its two opposite rectangular faces will be ___________ × 10⁻⁷ Ω.

Solution

Physics sir · 3 steps

Pick the right pair of faces first: current flows across the 1 cm gap through a big 1 cm by 100 cm face.

1. Which faces. The block has two square faces (1 cm × 1 cm) and four rectangular faces (1 cm × 100 cm). Two opposite rectangular faces are only 1 cm apart.
2. Length and area. Current flows between these faces, so the length is l = 1 cm = 10⁻² m. The area it flows through is the face itself: A = 10⁻² m × 1 m = 10⁻² m².

   R = (ρ l)/A = (3 × 10⁻⁷ × 10⁻²)/10⁻² Ω

3. So. R = 3 × 10⁻⁷ Ω, so the answer is 3.

The common slip: 30000. Taking the square end faces instead uses l = 1 m and A = 10⁻⁴ m², giving 3 × 10⁻³ Ω, which is 30000 in units of 10⁻⁷ Ω.

The idea to keep. In R = ρ l/A, the length is the distance between the two faces you connect, and the area is the area of those faces. Short and wide means small resistance.

Answer from the NTA final answer key. Solution by PrepWiser.