First slide

Electrical power

Question

A cell sends a current through a resistance R₁, for one second and then sends current through another resistance R₂ for one second. Same heat is produced in both the resistances. The internal resistance of the cell is

Moderate

A

R₁-R₂
B

R₂ +R₂
C

$\sqrt{(R_{1} R_{2})}$
D

$\sqrt{(R_{1}^{2} - R_{2}^{2})}$

Solution

$i_{1} = \frac{E}{R_{1} + r} and i_{2} = \frac{E}{R_{2} + r}$
Also $i_{1}^{2} R_{1} = i_{2}^{2} R_{2}$
$∴ \frac{E^{2} R_{1}}{{(R_{1} + r)}^{2}} = \frac{E^{2} R_{2}}{{(R_{2} + r)}^{2}}$
Solving, we get r $= \sqrt{R_{1} R_{2}}$

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