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 ..................... $A$.

Twelve equal resistors,each of resistance $R$,are connected to form a skeleton cube. The equivalent resistance between two diagonally opposite corners is:

In a Wheatstone network,$P=2 \Omega, Q=2 \Omega, R=2 \Omega$,and $S=3 \Omega$. The resistance with which $S$ is to be shunted so that the bridge may be balanced is: (in $\Omega$)

Consider the following two statements.
$(A)$ Kirchhoff's junction law follows from the conservation of charge.
$(B)$ Kirchhoff's loop law follows from the conservation of energy.
Which of the following is correct?

The value of current $I$ in the given circuit is (in $A$)

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