Internal resistance of a $12 \mathrm{V}$ car battery is $0.02 \mathrm{\Omega }$. What is the theoretical maximum power which it can deliver?

For the network shown in figure, the resistance between points $A$ and $B$ will be,

What is the potential difference between the points $A$ and $B$ ?

In the circuit shown in the given figure, the heat produced in the $5 \mathrm{\Omega }$ resistor due to a current flowing in it is $10 \mathrm{cal} {\mathrm{s}}^{-1}$. The heat produced in the $4 \mathrm{\Omega }$ resistor is

Two resistances $R_1$ and $R_2$ are joined as shown in the figure, to two batteries of emf $E_1$ and $E_2$. If $E_2$ is short-circuited the current through $R_1$ is