A cell develops the same power across two resistance R1 and R2 separately. The internal resistance of the cell is

Q: A cell develops the same power across two resistance R1 and R2 separately. The internal resistance of the cell is

Sol. Let r be the internal resistance of the cell and E its EMF. When connected across the resistance R1 in the circuit, current passing through the resistance is

$\large i = \frac{E}{R_1 + r}$

$\large P_1 = (\frac{E}{R_1 + r})^2 R_1 $

Similarly , $\large P_2 = (\frac{E}{R_2 + r})^2 R_2 $

Given that P1 = P2

Substituting the values, we get ;

$\large r = \sqrt{R_1 R_2} $