Currrent flows through a constriction conductor. The diameter and current density in the left of connection are `2.0mm and 1.3 xx 10^(6)Am^(-2)` (i) How much current flow through the constriction ? (ii) If the current density is tripled as it emerges from the right side of the constriction, what is the diameter of the hand is the diameter. of the right hand side of constriction?

Answer

(i)`4.09 A`(ii)1.15 mm`

Explanation

Let `D_(1) and D_(2)` be the diameter on the left hand side right hand side of combination. Then `D_(1) = 2.0 mm = 2 xx 10^(3)m, J_(1) = 1.3 xx 10^(6) Am^(-2)`
(i) current flowing through the constriction
`I_(1) = J_(1) A_(1) = J_(1) (pi D_(1)^(2))/(4) = (1.3 xx 10^(6)) xx (22)/(7) xx ((2 xx 10^(-3))^(2))/(4)`
` = 4.09 A`
(ii) For a steady flow of current, `I_(1) = I_(2)`
or `J_(1)A_(1) = J_(2)A_(2)`
or `J_(1) (pi D_(1)^(2))/(4) = J_(2) (pi D_(2)^(2))/(4) = 3 J_(1) (pi D_(2)^(2))/(4)`
or `D_(2) = (D_(1))/(sqrt(3)) = (2.0 "mm")/(sqrt(3)) = 1.15 "mm"`