Calculate the equivalent resistance across $A-B$ in the given circuit. ............... $\Omega$

$A$ circular coil of total resistance $40 \Omega$ has two points '$P$' and '$Q$' on its circumference. The arc length between '$P$' and '$Q$' is such that the coil is divided into two parts with resistances $30 \Omega$ and $10 \Omega$. These points are connected to a $16 \text{ V}$ battery with an internal resistance of $0.5 \Omega$. What is the value of the current '$I$' flowing through the circuit (in $\text{ A}$)?

Resistors $R, 2R, 4R, 8R, ..... \infty$ are connected in parallel. What is their equivalent resistance?

Resistors of $4\, R, 16\, R, 64\, R, \dots \infty$ are connected in series. Find their equivalent resistance.

Two wires of same metal have the same length but their cross-sections are in the ratio $3:1$. They are joined in series. The resistance of the thicker wire is $10\,\Omega$. The total resistance of the combination will be ............. $\Omega$.

In the given circuit,the current flowing through the resistance $20 \ \Omega$ is $0.3 \ A$,while the ammeter reads $0.9 \ A$. The value of $R_1$ is . . . . . . $\Omega$.