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A cell sends a current through a resist...

A cell sends a current through a resistance `R_(1)` for time `t`, next the same cell sends current through another resistance `R_(2)` for the time `t` If the same amount of heat is developed in both the resistance then find the internal resistance of the cell

A

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

B

`sqrt(r_(1)R_(2)). (2sqrt(R_(2)) - sqrt(R_(1)))/(sqrt(R_(2))-2sqrt(R_(1)))`

C

`sqrt(R_(1)R_(2)).(sqrt(R_(2))-2sqrt(R_(1)))`

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
`H= i^(2)Rt`
`=(E/(r + R_(1))^(2) (R_(1)t)`

`4H = (E/(r + R_(2))^(2)) (R_(2)t))`
`1/4 =(1/(r + R_(1))) R_(1) xx (r + R_(2))^(2)/R_(2)`
`rArr sqrt(R_(2))(R_(1) +r) = 2sqrt(R_(1)) (R_(2) + r)`
`sqrt(R_(1)R_(2)) (2sqrt(R_(2)) - sqrt(R_(1)))/(sqrt(R_(2))- 2sqrt(R_(1)))`
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