When two identical batteries of internal resistance $1 \Omega$ each are connected in series across a resistor $R$, the rate of heat produced in $R$ is $P_1$. When the same batteries are connected in parallel across $R$, the rate of heat produced is $P_2$. If $P_1=2.25 P_2$, then the value of $R$ is

The potential difference across a conducting wire of length 20 cm is 30 V . If the electron mobility is $2 \times 10^{-6} \mathrm{~m}^2 \mathrm{~V}^{-1} \mathrm{~s}^{-1}$, then the drift velocity of the electrons is

A maximum current of 0.5 mA can pass through a galvanometer of resistance $15 \Omega$. The resistance to be connected in series to the galvanometer to convert it into a voltmeter of range $0-10 \mathrm{~V}$ is

A part of a circuit is shown in the figure. The ratio of the potential differences between the points $A$ and $C$ and the points $D$ and $E$ is