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A battery of emf E and internal resistan...

A battery of emf `E` and internal resistance `r` is connected to a resistor of restance `r_(1)` and Q Joules of heat is produced in a certain time `t`. When the same battery is connected to another resistor of resistance `r_(2)` the same quantity of heat is produced in the same time `t`. Then the value of `r` is

A

`(r_(1) ^(2) )/(r_(2))`

B

`(r_(2) ^(2))/(r_(1))`

C

`1/2 (r_(1) + r_(2))`

D

`sqrt(r_(1)r_(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
`Q = V^(2)/r_(1) = (E^(2)r_(1))/(r + r_(1))^(2)
Q = V^(2)/r_(2) = (E^(2).r_(2))/(r + r_(2))^(2)`
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