In the circuit shown below,$E_1 = 4.0 \,V, R_1 = 2 \,\Omega, E_2 = 6.0 \,V, R_2 = 4 \,\Omega$ and $R_3 = 2 \,\Omega$. The current $I_1$ is ..................... $A$.

In a Wheatstone bridge (see figure),resistances $P$ and $Q$ are approximately equal. When $R = 400 \,\Omega$,the bridge is balanced. On interchanging $P$ and $Q$,the value of $R$ for balance is $405 \,\Omega$. The value of $X$ is close to ................. $\Omega$. (in $.5$)

In the given circuit,it is observed that the current $I$ is independent of the value of the resistance $R_6$. Then the resistance values must satisfy

Seven resistances are connected as shown in the figure. The equivalent resistance between $A$ and $B$ is ............... $\Omega$.

Four resistances of $15\, \Omega, 12\, \Omega, 4\, \Omega$ and $10\, \Omega$ are connected in cyclic order to form a Wheatstone bridge network. The resistance that is to be connected in parallel with the resistance of $10\, \Omega$ to balance the network is ................. $\Omega$.

In the following electrical network, the value of $I$ is (in $\text{ A}$)