Question

a cell of constant emf first connect to a resistance R1 and then to connected to the reskstance R2 0. If power delivered in both cases is the same then the internal resistance of the cell :

Answer 1

The cell has constant emf

Resistance is R1 and R2

P = V2 / R1 + r

P = V2 / R2 - r

( R1 - R2 ) / 2

The internal resistance of the cell is ( R1 - R2 ) / 2

Answer 2

Internal resistance r=(R1*R2)^1/2

 

This is obtained from: Current in the circuit for R1 connected => i = V/(R1 +r)

Hence power dissipated by R1 => P1 =  

\frac{V^{2}}{ (R1 + r)^{2}} * R1              {P = i2 R}

 

The power dissipated across both R1 and R2 is same.

\frac{R_{1}}{(R_{1} + r)^{2}} = \frac{R_{2}}{ (R_{2} + r)^{2}}

 

Solve these by taking R1/R2 on one side, take its square root, Dividendo on RHS. Then r will simply come out to be (R1R2)1/2