Refer to the circuit diagram given below. The heat generated across the $6\text{ }\Omega$ resistance in $100\text{ s}$ is $\frac{\alpha}{100}\text{ J}$. The value of $\alpha$ is . . . . . . . (Nearest integer)

If the charge on the capacitor is $1 \text{ mC}$ in the given circuit,then $\frac{R_1 R_2}{R_3} = \ldots \ldots \ldots \Omega$.

Calculate the equivalent resistance between $A$ and $B$.

What is the value of $i_3$ in the given circuit?

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

$ABCD$ is a square where each side is a uniform wire of resistance $1\,\Omega$. $A$ point $E$ lies on $CD$ such that if a uniform wire of resistance $1\,\Omega$ is connected across $AE$ and a constant potential difference is applied across $A$ and $C$,then $B$ and $E$ are equipotential.