Question

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

• A. 1.28 W
• B. 2.0W
• C. 8/9 W
• D. 3.2 W

Answer 1

The correct option is B 2.0W

Here two internal resistances are in parallel so equivalent internal resistance $r_{eq}=1||1=\frac{1\times 1}{1+1}=1/2=0.5\Omega$
According to maximum power theorem the power will be max when internal resistance is equal to external resistance. since, $r_{eq}=R=0.5\Omega$
Maximum current through R is $I_{max}=\frac{V}{r_{eq}+R}=\frac{2}{0.5+0.5}=2A$
Maximum power is $P_{max}=I_{max}^{2}R=2^2\times 0.5=2W$