If a steady current I is flowing through a cylindrical element ABC. Choose the correct relationship

Options

A. `V_(AB) = 2V_(BC)`
B. power across BC is 4 times the power across AB.
C. Current densities in AB and BC are equal.
D. Electric field due to current inside AB and BC are equal

Answer

B

Explanation

(b)
(a) V_(AB)/V_(BC) = (I_(AB)R_(AB))/(I_(BC)R_(BC)) = R_(AB)/R_(BC) = (rho l/(2[pi xx 4r^2]))/(rhol/(2[pir^2])) = 1/4`
`[I_(AB) = I_(BC), wire is of same material ]
Therefore option (a) is incorrect.
(b) `P_(BC)/P_(AB) = (I^2R_(BC))/(I^2R_(AB)) = (rho l/(2[pi xx 4r^2]))/(rhol/(2[pir^2])) = 1/4 `
`:. P_(AB) = 4P_(BC) , Therefore (b) is correct.
(c) J_(AB)/J_(BC) = (I/(pi xx 4r^2)) /(I/(pi xx r^2)) = 1/4 `, Therefore (c) is incorrect.
(d) `E_(AB)/E_(BC) = [(V_(AB)/(l//2))]/[(V_(BC)/l//2)] = 1/4`, Therefore (d) id incorrect.