The current flowing in the given circuit is $0.1\,A$. The potential difference between the points $X$ and $Y$ is ................ $V$.

Resistors of $1\, \Omega$, $2\, \Omega$, and $3\, \Omega$ are connected in the form of a triangle. If a $1.5\, V$ cell of negligible internal resistance is connected across the $3\, \Omega$ resistor, the current flowing through this resistance will be ................ $A$.

$A$ galvanometer of resistance $G$ is connected in a circuit. Now,a resistance $R$ is connected in series with the galvanometer. To keep the main current in the circuit unchanged,the resistance $S$ to be put in parallel with the series combination of $G$ and $R$ is:

The electrochemical equivalents of $Cu$ and $Ag$ are $7 \times 10^{-6}$ and $1.2 \times 10^{-6}$ respectively. If a certain current deposits $14 \ g$ of $Cu$,then the amount of $Ag$ deposited is .......... $g$.

In the adjacent circuit,a voltmeter of internal resistance $R$,when connected across $B$ and $C$,reads $\frac{100}{3} \ V$. Neglecting the internal resistance of the battery,the value of $R$ is ................. $k \Omega$.

Consider a circuit where a cell of emf $E_0$ and internal resistance $r$ is connected across the terminals $A$ and $B$ as shown in the figure. The value of $R$ for which the power generated in the circuit is maximum is given by