A metel rod of the length 10cm and a rectangular cross-section of 1 cm xx `1//2` cm is connected to a battery across opposite faces. The resistance will be

Options

A. maximum when the battery is connected across `1 cm xx 1//2` can faces
B. maximum when the battery is connected across `10xx 1cm` faces
C. maximum when the battery is connected across 10 cm `xx1//2` cm faces
D. same irrespective of the three faces

Answer

A

Explanation

We know that `R-(pl)/(A)`
(a) When the battery is connected across `1 cm xx 1//2` cm faces,
then `l=10cm, A=1xxcm^(2),R_(1)=(pxx10)/(1xx1//2)=20 p Omega`
(b) When the battery is connected across 10 cm xx 1 cm faces,
then `l=1//2 cm, A=10xx1 cm^(2), R_(2)=(pxx1//2)/(10xx1)=(p)/(20)Omega`
(C) When the battery is connected across 10cm xx 1//2c, faces.
then `l=1cm, A=10xx1//2 cm^(2), R_(3)=(pxx1)/((10xx1//))=(p)(5)Omega`