In the circuit shown in the figure, calculate the following:

(a) Potential difference between points $a$ and $b$ when switch $S$ is open.

(b) Current through $S$ in the circuit when $S$ is closed.

In this circuit, if ${\epsilon }_1=6 \mathrm{V}, {\epsilon }_2=3 \mathrm{V}, R_1=2 \mathrm{\Omega }$ and $R_2=R_3=3 \mathrm{\Omega }$, find the current through each cell and resistors.

In the given circuit, $R_1=1 \mathrm{\Omega }, R_2=2 \mathrm{\Omega }, R_3=2 \mathrm{\Omega }, R_4=1 \mathrm{\Omega }, r=\frac{2}{3} \mathrm{\Omega }$ and $\epsilon =10 \mathrm{V}$. Find,

(a) Total current drawn from the battery.

(b) Current in the wire $AB.$

Calculate the value of the electric currents $I_1, I_2$ and $I_3$ in the given electrical network.
(a) $I_1=$ ________

(b) $I_2=$ ________

(c) $I_3=$ ________

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.