Three resistors having resistances $r_{1}, r_{2}$ and $r_{3}$ are connected as shown in the given circuit. The ratio $\frac{i_{3}}{i_{1}}$ of currents in terms of resistances used in the circuit is :

Find the value of the current from the battery in the circuit shown in the figure. (in $A$)

$A$ coil of $100 \, W, 220 \, V$ is cut into two equal parts and connected in parallel. How much heat in $J$ is produced in $1 \, sec$?

$A$ battery has an $e.m.f.$ of $4 \ V$ and an internal resistance of $r$. When the battery is connected to an external resistance of $2 \ \Omega$,a current of $1 \ A$ flows through the circuit. If the terminals of the battery are short-circuited (connected directly),what will be the current in $A$ flowing through it?

$A$ battery of $e.m.f.$ $10\, V$ is connected to a resistance network as shown in the figure. The potential difference ${V_A} - {V_B}$ between the points $A$ and $B$ is .................... $V$.

When a resistor of $11 \Omega$ is connected in series with an electric cell,the current flowing in it is $0.5 \ A$. Instead,when a resistor of $5 \Omega$ is connected to the same electric cell in series,the current increases by $0.4 \ A$. The internal resistance of the cell is (in $\Omega$)