A metal rod of length 10 cm and a rectangular cross-section of 1 cm×1/2 cm is connected to a battery across opposite faces. The resistance will be _.

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(2) Maximum when the battery is connected across the 1 cm×1/2 cm faces.. Idea: R=ρL/A, where L is the length along the current and A is the area of the pair of faces the battery is connected across. Across the 1 cm×1/2 cm faces: L=10 cm, A=0.5 cm², so L/A=20 cm⁻¹. Across the 10 cm×1/2 cm faces: L=1 cm, A=5 cm², so L/A=0.2 cm⁻¹. Across the 10 cm×1 cm faces: L=0.5 cm, A=10 cm², so L/A=0.05 cm⁻¹. The longest path through the smallest area gives the largest resistance: the 1 cm×1/2 cm faces.

A metal rod of length 10 cm and a rectangular cross-section of 1 cm×1/2 cm is connected to a battery across opposite faces. The resistance will be _________.

Step-by-step solution

Why the other options are wrong