A metal rod of the length 10cm and a rectangular cross-section of 1cm X 1/2cm faces. Calculate the resistance
a) When battery is connected across 1cm X 1/2 cm faces.
b) When battery is connected across 10cm X 1 cm faces.

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Solution

$L e t ρ b e t h e d e n s i t y o f t h e m e t a l r o d . W h e n w e c o n n e c t t h e b a t t e r y b e t w e e n t h e f a c e 1 \times 1 / 2 c m^{2}, t h e n a a r e a o f c r o s s e c t i o n i s 1 \times 1 / 2 = 0.5 c m^{2} = 0.00005 m^{2} l e n g t h o f t h e c o n d u c t o r = 10 c m = 0.1 m r e s i s \tan c e = \frac{ρ \times l e n g t h}{a r e a} = \frac{ρ \times 0.1}{0.00005} = ρ \times 2000 o h m W h e n b a t t e r y i s c o n n e c t e d b e t w e e n t h e f a c e 1 \times 10 t h e n a r e a o f c r o s s e c t i o n = 1 \times 10 = 10 c m^{2} = 0.001 m^{3} l e n g t h = 0.5 c m = 0.005 m r e s i s \tan c e = \frac{ρ \times 0.001}{0.005} = \frac{ρ}{5} o h m$

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