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A battery of EMF E produces currents 4 A...

A battery of EMF E produces currents 4 A and 3 A when connected to external resistance ` 1 Omega` and `2 Omega` respectively. The internal resistance of the battery is

A

`(I_(1)R_(2) - I_(2)R_(1))/(I_(2) - I_(1))`

B

`(I_(1)R_(2)+ I_(2)R_(1))/(I_(1) - I_(2))`

C

`(I_(1)R_(1) + I_(2)R_(2))/(I_(1) - I_(2))`

D

`(I_(1)R_(1) - I_(2)R_(2))/(I_(2)-I_(1))`

Text Solution

Verified by Experts

The correct Answer is:
D
`I_(1) = E/(r +R(1)), I_(2) =E/(r +R_(2))`
`rArr I_(1)(r + R_(1)) = I_(2) (r+R_(2))`
`rArr r(I_(1)-I_(2)) =I_(2)R_(2) - R_(1)I_(1)`
`r = (I_(1)R_(1) - I_(2)R_(2))/(I_(2)-I_(1))`
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