An infinite ladder network is arranged with resistances $R$ and $2R$ as shown. The effective resistance between terminals $A$ and $B$ is

$A$ battery of $e.m.f.$ $3\, V$ and internal resistance $1.0\, \Omega$ is connected in series with a copper voltameter. The current flowing in the circuit is $1.5\, A$. The resistance of the voltameter will be ........... $\Omega$.

In the given circuit,the power generated in the $1 \, \Omega$ resistance will be maximum for $x$ equal to ................ $\Omega$.

$A$ voltmeter is connected in parallel with a variable resistance $R$ which is in series with an ammeter and a cell as shown in the figure. For one value of $R$,the meters read $0.3 \, A$ and $0.9 \, V$. For another value of $R$,the readings are $0.25 \, A$ and $1.0 \, V$. What is the internal resistance of the cell in $\Omega$?

What is the current $I$ (in $A$) flowing through the given circuit?

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: