Determine current in $3 \Omega$ resistance and potential difference between $A$ and $B$ in the adjoining circuit diagram.

In the circuit shown in figure, $E_1=17 V, E_2=21 V, R_1=2\Omega , R_2=3\Omega$ and $R_3=5\Omega$. Using Kirchhoff's laws, find currents flowing through resistors $R_1, R_2$ and $R_3$  (internal resistance of each of the batteries is negligible)

In the given circuit $E_1$ and $E_2$ are two cells of emfs $2 V$ and $3 V$ respectively, having negligible internal resistances. Applying Kirchhoff’s laws of electrical networks, find the values of $I_1$ and $I_2$.

Two cells $E_1$ and $E_2$ of emf's $4 \mathrm{V}$ and $2 \mathrm{V}$ respectively, each having an internal resistance of $2\Omega$ send current in an external resistance of $8\Omega$. Find the magnitudes and the directions of currents $I_1$ and $I_2$ flowing through the cells $E_1$ and $E_2$.

Calculate the currents $I_1,I_2$ and $I_3$ in the given The cells have negligible internal resistances.