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# A battery of emf 'E' and internal resistance 'r' is connected to a resistor of resistance $'r_1'$ 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 :

$\begin {array} {1 1} (1)\;\large\frac{r_2^2}{r_1} & \quad (2)\;\large\frac{1}{2}(r_1+r_2) \\ (3)\;\sqrt{r_1r_2} & \quad (4)\;\large\frac{r_1^2}{r_2} \end {array}$

(3) $\sqrt{r_1r_2}$