A parallel combination of an $8 \mathrm{\Omega }$ resistor and an unknown resistor $R$ is connected in series with a $16 \mathrm{\Omega }$ resistor and a battery. This circuit is then disassembled, and the three resistors are then connected in series with each other and the same battery. In both arrangements, the current through the $8 \mathrm{\Omega }$ resistor is the same. What is the unknown resistance $R$?

For the resistor network shown in figure, the potential drop between $a$ and $b$ is $12 \mathrm{V}$.

(a) Current through resistance of $6 \mathrm{\Omega }$ is ________.

(b) Current through resistance of $2 \mathrm{\Omega }$ is ________ .

(c) Current through resistance of $8 \mathrm{\Omega }$ is ________ .

In an experiment, a graph (figure) was plotted of the potential difference $V$ between the terminals of a cell against circuit current $I$ by varying load rheostat. Find the internal conductance of the cell.
(a) 

(b) 

Each resistance in the circuit (figure) is of $2000 \mathrm{\Omega }$.

The combination is put across a supply of $200 \mathrm{V}$. Find the reading of the ammeter.

A hemispherical network of radius $a$ is made by using a conducting wire of resistance per unit length $r$. Find the equivalent resistance across $OP$.

If each of the resistances in the shown network is $R$, then what is the resistance between $A$ and $B$.

Consider the circuits shown in figure. Both the circuits are taking same current from the battery, but the current through $R$ in the second circuit is ${\left(\frac{1}{10}\right)}^{\mathrm{th}}$ of the current through $R$ in the first circuit. If $R$ is $11 \mathrm{\Omega }$, then find the value of $R_1$ and $R_2$.