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if a cell of constant electromotive force produces the same amount of heat during the same time in two independent resistances R1 and R2, when connected separately one after the other, across the cell, what is the internal resistance of the cell

if a cell of constant electromotive force produces the same amount of heat during the same time in two independent resistances R1 and R2, when connected separately one after the other, across the cell, what is the internal resistance of the cell

Grade:12th pass

1 Answers

Piyush Maheshwari
44 Points
6 years ago
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

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