Question

Two identical batteries each of e.m.f 2 V and internal resistance $1\, \Omega$ are available to produce heat in an external resitance by passing a current through it. The maximum power that can be developed across R using these batteries is

• A. 3.2 W
• B. 2.0 W
• C. 1.28 W
• D. $\frac{8}{9} W$

Answer 1

Answer: (B)

2.0 W

Answer 2

For maximum current, the two batteries should be connected in series. The current will be maximum when external resistance is equal to the total internal resistance of cells i.e.$2\, \Omega$.
Hence power developed across the resistance R will be

$\, \, \, \, \, I^2R=\bigg(\frac{2E}{R+2r}\bigg)^2 \, \, R=\bigg(\frac{2 \times 2}{2+2}\bigg)^2 \times 2 = 2\, W$