If the Wheatstone bridge shown in the figure is balanced,then the values of $R_1$ and $R_2$ are ...... $\Omega$ and ...... $\Omega$ respectively.

In the circuit shown,the currents (in $A$) through the $50\; V$ and $30\; V$ batteries are,respectively:

In the circuit shown in the figure,when no current flows through the $5\,\Omega$ resistor,the value of the resistor $X$ will be ........... $\Omega$.

In the adjoining circuit,the battery $E_1$ has an $e.m.f.$ of $12 \, V$ and zero internal resistance,while the battery $E$ has an $e.m.f.$ of $2 \, V$. If the galvanometer $G$ reads zero,then the value of the resistance $X$ in $\Omega$ is

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 $\text{ A}$)

See the electrical circuit shown in this figure. Which of the following equations is a correct equation for it?