Use Kirchhoff’s rules to determine the value of the current $I_1$ flowing in the circuit shown in Fig.

 

Using Kirchhoff’s laws, determine the currents $I_1$, $I_2$ and $I_3$ for the network shown in Fig.

The circuit diagram shown in Fig. has two cells ${\xi }_2$ and ${\xi }_2$ with emfs $4 \mathrm{V}$ and $2 \mathrm{V}$ respectively, each one having an internal resistance of $2 \mathrm{\Omega }$. The external resistance $R$ is of $8 \mathrm{\Omega }$. Find the magnitude and direction of currents flowing through the two cells.

Fig. shows n cells connected to form a series circuit. Their internal resistances are related to their emfs as $r_i=\alpha {\xi }_i$, where α is a constant. Find the current through the circuit.

Fig. shows n cells connected to form a series circuit. Their internal resistances are related to their emfs as $r_i=\alpha {\xi }_i$, where α is a constant. Find the potential difference between the terminals of $i$th battery.

Two cells of emfs $3 \mathrm{V}$ and $4 \mathrm{V}$ and internal resistances $1 \mathrm{\Omega }$ and $2 \mathrm{\Omega }$ respectively are connected in parallel so as to send current in the same direction through an external resistance of $5 \mathrm{\Omega }$.

Draw the circuit diagram.

Two cells of emfs $3 \mathrm{V}$ and $4 \mathrm{V}$ and internal resistances $1 \mathrm{\Omega }$ and $2 \mathrm{\Omega }$ respectively are connected in parallel so as to send current in the same direction through an external resistance of $5 \mathrm{\Omega }$.

Using Kirchhoff’s laws, calculate (a) the current through each branch of the circuit. (b) p.d. across the $5 \mathrm{\Omega }$ resistance.

In the electric network shown in Fig, use Kirchhoff’s rules to calculate the power consumed by the resistance $R=4 \mathrm{\Omega }$.

A network of resistors is connected to a battery of negligible internal resistance, as shown in Fig. Calculate the equivalent resistance between the points $A$ and $D$, and the value of the current $I_3$.