In the given circuit,the resistance of the voltmeter is $10,000\, \Omega$ and the resistance of the ammeter is $20\, \Omega$. The ammeter reading is $0.1\, \text{A}$. If the voltmeter reading is $12\, \text{V}$,then the value of $R$ is ............ $\Omega$.

Two bulbs $X$ and $Y$ have the same voltage rating and their power ratings are $40 \ W$ and $60 \ W$ respectively. They are connected in series to a $300 \ V$ battery as shown in the figure. Then:

$A$ battery of $e.m.f.$ $E$ and internal resistance $r$ is connected to a variable resistor $R$ as shown in the figure. Which one of the following is true?

$A$ uniform wire of resistance $9 \, \Omega$ is cut into $3$ equal parts. They are connected in the form of an equilateral triangle $ABC$. $A$ cell of $e.m.f.$ $2 \, V$ and negligible internal resistance is connected across $B$ and $C$. The potential difference across $AB$ is ............... $V$.

Two resistors whose values are in the ratio $2 : 1$ are connected in parallel with one cell. The ratio of power dissipated is:

When a resistor of $11 \Omega$ is connected in series with an electric cell,the current flowing in it is $0.5 \ A$. Instead,when a resistor of $5 \Omega$ is connected to the same electric cell in series,the current increases by $0.4 \ A$. The internal resistance of the cell is (in $Omega$)