Question

For maximum power delivered to the external circuit by the battery, the internal resistance of battery r is

Answer 1

Answer:

when power delivered is max then the equivalent resistance of the external circuit is equal to the internal resistance of the battery

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Answer 2

• We know, for maximum power

• internal resistance (r) = equivalent resistance($R_{eq}$)

                                 r = $R_{eq}$

• ∴ we have to find $R_{eq}$ for entire circuit.

           $R_{eq_{1} } = 2R$ for serial combination'

• Now agani we simplify,

• $R_{eq} _{2} =\frac{(R)(2R)}{R+2R}$    for parallel.

                $=\frac{2R^{2} }{3R}$

               $=\frac{2R}{3}$

• $R_{eq} _{3} =\frac{2R}{3} +\frac{2R}{3}$

               $=\frac{4R}{3}$

• Now for figure D resistor is connected in parallel,

          ∴ $R_{eq}=\frac{(\frac{2R}{3})(\frac{4R}{3} ) }{(\frac{2R}{3}) + (\frac{4R}{3} )}$

                    $=\frac{4R}{9}$   $=r$

∴  maximum power delivered to the external circuit by the battery, the internal resistance of battery r is$\frac{4R}{3}$