Question

Two identical batteries each of emf $E=2V$ and internal resistance $r=1\Omega$ are available to produce heat in an external circuit. What is the maximum rate of production of heat that can be obtained in the external circuit?

• A. 1 W
• B. 2 W
• C. 4 W
• D. 8 W

Answer 1

The correct option is B 2 W

We assume both the batteries be connected in series. According to maximum power theorem, the power will be maximum when the external resistance (load resistance) is equal to the total internal resistance of the cells.
i.e $R=r+r=2r=2\times 1=2\Omega$
Now the current in the circuit is: $I=\frac{E+E}{R+2r}=\frac{2+2}{2+2}=1A$
Thus, maximum power in the external circuit is $P_{max}=I^{2}R=1^2\left(2\right)=2W$