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# A battery of internal resistance $2 \Omega$ is connected to a variable resistor whose value can be varied from $4\Omega\: to\: 10\Omega$. If the variable resistance is gradually increased from an initial value of $4\Omega$, the power consumed by it:

$\begin {array} {1 1} (A)\;Will \: decrease \: monotonically \\ (B)\;Will\: increase\: monotonically \\ (C)\;May \: increase\: or\: decrease\: depending\: on\: the\: EMF\: of\: the\: battery \\ (D)\;Will \: first\: increase \: to\: a\: maximum\: value\: and\: the\: monotonically\: decrease. \end {array}$

Can you answer this question?

By maximum power theorem, maxima in the power vs. resistance curve occurs when internal resistance =
external resistance. Beyond this point the graph is monotonically decreasing.
Ans : (A)
answered Feb 10, 2014
edited Mar 14, 2014