$A$ potential divider is used to give outputs of $4\, V$ and $8\, V$ from a $12\, V$ source. Which combination of resistances $(R_1, R_2, R_3)$ gives the correct voltages? Find the ratio $R_1 : R_2 : R_3$.

An ammeter and a voltmeter of resistance $R$ are connected in series to an electric cell of negligible internal resistance. Their readings are $A$ and $V$ respectively. If another resistance $R$ is connected in parallel with the voltmeter, what happens to the readings $A$ and $V$?

Three resistors $1 \Omega, 2 \Omega$ and $3 \Omega$ are connected to form a triangle. Across the $3 \Omega$ resistor,a $3 \text{ V}$ battery is connected. The current through the $3 \Omega$ resistor is: (in $\text{ A}$)

The potential difference across the $8\ \Omega$ resistance is $48\ V$ as shown in the figure. The value of the potential difference across points $X$ and $Y$ will be ............... $V$.

If the galvanometer reading is zero,then the resistance $X = \dots \Omega$.

$A$ cell of $e.m.f.$ $1.5\,V$ having a finite internal resistance is connected to a load resistance of $2\,\Omega$. For maximum power transfer,the internal resistance of the cell should be ............. $\Omega$.