In an experiment on a circuit as shown in the figure, the voltmeter shows $8 \,V$ reading. The resistance of the voltmeter is,

Three resistors of $4\,\Omega$,$6\,\Omega$,and $12\,\Omega$ are connected in parallel,and the combination is connected in series with a $1.5\,V$ battery of $1\,\Omega$ internal resistance. The rate of Joule heating in the $4\,\Omega$ resistor is ................ $W$.

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

$A$ battery of $e.m.f.$ $10 \, V$ and internal resistance $3 \, \Omega$ is connected to a resistor $R$ as shown in the figure. If the current in the circuit is $0.5 \, A$,then the resistance of the resistor $R$ will be ............. $\Omega$.

In the following circuit diagram,$E = 4\,V, r = 1\,\Omega$ and $R = 45\, \Omega$,then the reading of the ammeter $A$ will be

$A$ battery of $e.m.f.$ $10\, V$ and internal resistance $0.5\, \Omega$ is connected across a variable resistance $R$. The value of $R$ for which the power delivered in it is maximum is given by ......... $\Omega$.