An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the length and radii of the wires are in the ratio of 4/3 and 2/3, then the ratio of the currents passing through the wire will be

3

1/3

8/9

2

Solution

1/3

straight I subscript 1 over straight I subscript 2 space equals space straight R subscript 1 over straight R subscript 2 left square bracket Current space divider space rule space since space voltage space is space same space in space parallel right square bracket straight I subscript 1 over straight I subscript 2 space equals space straight L subscript 2 over straight L subscript 1 space straight x space fraction numerator straight r subscript 1 superscript 2 over denominator straight r subscript 2 superscript 2 end fraction therefore comma space straight I subscript 1 over straight I subscript 2 space equals space 3 over 4 space straight x space open parentheses 2 over 3 close parentheses squared space equals space 1 third

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