$A$ filament bulb $(500 \,W, 100 \,V)$ is to be used in a $230 \,V$ main supply. When a resistance $R$ is connected in series,it works perfectly and the bulb consumes $500 \,W$. The value of $R$ is .................. $\Omega$.

Two cells of same $emf$ $E$ but internal resistances $r_1$ and $r_2$ are connected in series to an external resistor $R$ (as shown in the figure). What should be the value of $R$ so that the potential difference across the terminals of the first cell becomes zero?

$A$ 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 ............. $\Omega$.

Two resistances of $400 \Omega$ and $800 \Omega$ are connected in series with a $6 \text{ V}$ battery of negligible internal resistance. $A$ voltmeter of resistance $10000 \Omega$ is used to measure the potential difference across the $400 \Omega$ resistor. The error in the measurement of potential difference in volts is approximately:

For the network of resistors shown in the figure,choose the correct option.

In the given circuit,$(V_A - V_B) = \dots \dots \dots V$.