Find the current in each wire.

Find the current assuming $R=10 \mathrm{\Omega }\text{,} {\mathrm{\epsilon }}_1=6 \mathrm{V}\text{,} r_1=1.5 \mathrm{\Omega }\text{,} {\mathrm{\epsilon }}_2=4 \mathrm{V}$ and $r_2=\frac{1}{2} \mathrm{\Omega }$.

Find the emf and internal resistance of the equivalent cell between $A$ and $B$. Put ${\epsilon }_1=6 \mathrm{V}$, $r_1=2 \mathrm{\Omega }\text{,} {\mathrm{\epsilon }}_2=4 \mathrm{V}\text{,} r_2=2 \mathrm{\Omega }$ and ${\epsilon }_3=3 \mathrm{V}$, $r_3=3 \mathrm{\Omega }$.

In the given network, find the

(a) potential difference between $a$ and $b$.

(b) Current in each branch.

In the given circuit in figure, all batteries have emf $10 \mathrm{V}$ and internal resistance is negligible. All resistors are in $\mathrm{ohm}$. Calculate the current in the right-most $2 \mathrm{\Omega }$ resistor.

In the given circuit, determine current through branch having indicated resistor $R_4$. Given $R_1=R_2=4\mathrm{\Omega },\mathrm{}{R}_3=R_4=R_5=2\mathrm{\Omega },{\mathrm{\epsilon }}_1=5\mathrm{V},\mathrm{}{\mathrm{\epsilon }}_2=10\mathrm{V}$

Determine current through batteries ${\epsilon }_1$, and ${\epsilon }_2$.

Find the equivalent resistance across terminals $P$ and $Q$ as shown in figure. Each resistance in circuit is $R$.