Two identical batteries each of e.m.f 2 V and internal resistance 1 Ω 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

Question

Two identical batteries each of e.m.f 2 V and internal resistance 1 Ω 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) (8/9) W

Tardigrade Admin · Accepted Answer

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 Ω

.
Hence power developed across the resistance

R

will be

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

Q. Two identical batteries each of e.m.f $2 V$ and internal resistance $1 Ω$ 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

3.2 W

2.0 W

1.28 W

$\frac{8}{9} W$

Q. Two identical batteries each of e.m.f 2V and internal resistance 1Ω 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

3.2 W

2.0 W

1.28 W

98​W

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. 2Ω. Hence power developed across the resistance R will be I2R=(R+2r2E​)2R=(2+22×2​)2×2=2W

Q. Two identical batteries each of e.m.f $2 V$ and internal resistance $1 Ω$ 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

$\frac{8}{9} W$