A cell of internal resistance $r$ is connected to an external resistance $R$. The power will be maximum in $R$, if 

The Wheat bridge shown in the figure is balanced. If the positions of the cell $C$ and the galvanometer $G$ are now interchanged, $G$ will show zero deflection 

A wire of length $L$ and $3$ identical cells of negligible internal resistances are connected in series. Due to the current, the temperature of the wire is raised by $\mathrm{\Delta }T$ in a time $t$. A number $N$ of similar cells are now connected in series with a wire of the same material and cross-section but of length $2L$. The temperature of the wire is raised by the same amount $\mathrm{\Delta }T$ in the same time $t$. The value of $N$ is

Calculate potential difference between points $d$ and $b$ in the circuit.