Two identical batteries, each of e.m.f. 2,V a | vedclass

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(B) For two identical batteries of $e.m.f.$ $E = 2\,V$ and internal resistance $r = 1.0\,\Omega$, we can connect them in series or parallel.Case $1$:

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$2$

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(B) For two identical batteries of $e.m.f.$ $E = 2\,V$ and internal resistance $r = 1.0\,\Omega$, we can connect them in series or parallel.Case $1$: Series connection.Total $e.m.f.$ $E_{eq} = 2E = 4\,V$.Total internal resistance $r_{eq} = 2r = 2.0\,\Omega$.Current $I = E_{eq} / (R + r_{eq}) = 4 / (0.5 + 2.0) = 4 / 2.5 = 1.6\,A$.Power $P = I^2 R = (1.6)^2 	imes 0.5 = 2.56 	imes 0.5 = 1.28\,W$.Case $2$: Parallel connection.Total $e.m.f.$ $E_{eq} = E = 2\,V$.Total internal resistance $r_{eq} = r/2 = 0.5\,\Omega$.Current $I = E_{eq} / (R + r_{eq}) = 2 / (0.5 + 0.5) = 2 / 1.0 = 2.0\,A$.Power $P = I^2 R = (2.0)^2 	imes 0.5 = 4.0 	imes 0.5 = 2.0\,W$.Comparing both cases, the maximum power is $2.0\,W$.

Two identical batteries, each of $e.m.f.$ $2\,V$ and internal resistance $1.0\,\Omega$, are available to produce heat in an external resistance $R = 0.5\,\Omega$ by passing a current through it. The maximum Joulean power that can be developed across $R$ using these batteries is ............. $W$.

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