Find the current flowing through the resistance $R_1$ of the circuit shown in the figure,if the resistances are equal to $R_1=10 \Omega, R_2=20 \Omega$,and $R_3=30 \Omega$,and the potentials of points $1, 2$,and $3$ are equal to $\phi_1=10 \text{ V}, \phi_2=6 \text{ V}$,and $\phi_3=5 \text{ V}$. (in $\text{ A}$)

Two cells of voltage $10 \ V$ and $2 \ V$ and internal resistances $10 \ \Omega$ and $5 \ \Omega$ respectively,are connected in parallel with the positive end of $10 \ V$ battery connected to the negative pole of $2 \ V$ battery (figure). Find the effective voltage and effective resistance of the combination.

The figure shows a network of currents. The magnitude of currents is shown in the diagram. The current $i$ will be ................. $A$.

The value of current through the $20\,\Omega$ resistor is .................. $A$.

In the balanced condition,the values of the resistances of the four arms of a Wheatstone bridge are shown in the figure below. The resistance $R_3$ has a temperature coefficient of $0.0004 \ {}^{\circ}C^{-1}$. If the temperature of $R_3$ is increased by $100 \ {}^{\circ}C$,the voltage developed between $S$ and $T$ will be. . . . . . . volt.

Four resistors $A, B, C$ and $D$ form a Wheatstone bridge. The bridge is balanced when $C = 100 \ \Omega$. If $A$ and $B$ are interchanged,the bridge balances for $C = 121 \ \Omega$. The value of $D$ is: (in $\Omega$)