Find the $emf$ $(E)$ of the cell in $V$ required to light the bulb rated $4.5 \, W, 1.5 \, V$ fully,as shown in the circuit.

Consider the circuit shown in the figure.

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

$A$ cell of emf $6\, V$ and internal resistance $0.5\, \Omega$ is short-circuited. The current in the cell is ............... $A$.

Find the current flowing through the resistance $R_2$ of the circuit shown in the figure,if the resistances are $R_1 = 20 \ \Omega, R_2 = 30 \ \Omega$ and $R_3 = 60 \ \Omega$,and the potentials of points $1, 2$ and $3$ are $V_1 = 20 \ V, V_2 = 30 \ V$ and $V_3 = 60 \ V$ respectively. (in $A$)

Two resistances ${R_1}$ and ${R_2}$ are connected as shown in the figure to two batteries of $e.m.f.$ ${E_1}$ and ${E_2}$. If ${E_2}$ is short-circuited,the current through ${R_1}$ is