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Question: A copper wire of length 1*m* and radius 1*mm* is joined in series with an iron wire of length 2*m* a...

A copper wire of length 1m and radius 1mm is joined in series with an iron wire of length 2m and radius 3mm and a current is passed through the wire. The ratio of current densities in the copper and iron wire is

A

18 : 1

B

9 : 1

C

6 : 1

D

2 : 3

Answer

9 : 1

Explanation

Solution

We know J=iAJ = \frac { i } { A } when i = constant J∝1AJ \propto \frac { 1 } { A }

⇒ JcJi=AiAc=(rirc)2=(31)2=91\frac { J _ { c } } { J _ { i } } = \frac { A _ { i } } { A _ { c } } = \left( \frac { r _ { i } } { r _ { c } } \right) ^ { 2 } = \left( \frac { 3 } { 1 } \right) ^ { 2 } = \frac { 9 } { 1 }