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The current enters at A and comes out at...

The current enters at A and comes out at D. Some of the resistance are shown. What should be resistance of wire CB so that it draws double of the current that enters the wire BF.

A

`((9)/(10))R`

B

`((8)/(9))R`

C

`((7)/(9))R`

D

`((3)/(20))R`

Text Solution

Verified by Experts

The correct Answer is:
D
Let current in AB be `I_(1)` in BF be `I_(2)` in BC be `2I_(2)`, in FC be `I_(3)`
in FE be `I_(3)` and in CD be `(I_(3) + 2I_(2))`
At point `B, I_(1) =3I_(2)`
At point `F, I_(2) = 2I_(3)`
Along ABFCD,
`V_(A) -V_(D) =V =I_(1) ((2R)/(5)) +I_(2)((R )/(5)) + I_(3) ((R )/(5)) + (I_(3)+2I_(2))(R )/(5) =2I_(2)R`
Along ABCD,
`V_(A) -V_(D) =V =2I_(2)R`
` =I_(1)((2R)/(5)) +2I_(2)R' +(I_(3) +2I_(2))(R )/(%)`
or `2I_(2)R' = (3)/(10)I_(2)R or R' =(3)/(20)R`
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