In an electric circuit shown in the figure, the external resistance R is variable. It is found that same power is developed in external resistance R if its value is either 5 Ω or 20 Ω. With this information find the internal resistance (r) of the voltage source.

A
$20 Ω$
B
$8 Ω$
C
$103 Ω$
D
$10 Ω$

Solution:

$\begin{array}{l} I = \frac{E}{R + r}, P = I^{2} R = \frac{E^{2} R}{{(R + r)}^{2}} \\ Now P_{1} = P_{2} \Rightarrow \frac{E^{2} 5}{{(5 + r)}^{2}} = \frac{E^{2} 20}{{(20 + r)}^{2}} \Rightarrow r = 10 Ω \end{array}$

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In an electric circuit shown in the figure, the external resistance R is variable. It is found that same power is developed in external resistance R if its value is either $5 Ω or 20 Ω$ . With this information find the internal resistance (r) of the voltage source.

Solution:

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