Each of the resistances in the network shown in the figure is equal to $R$. The resistance between the terminals $A$ and $B$ is

In an experiment, a graph was plotted of the potential difference $V$ between the terminals of a cell against the circuit current $i$ by varying the load rheostat. The internal conductance of the cell is given by:

In the given figure,the equivalent resistance between the points $A$ and $B$ is ............ $\Omega$.

$A$ storage battery of $emf$ $8.0\; V$ and internal resistance $0.5\; \Omega$ is being charged by a $120\; V$ $DC$ supply using a series resistor of $15.5\; \Omega$. What is the terminal voltage of the battery during charging? What is the purpose of having a series resistor in the charging circuit?

An electric bulb rated $500 \, W$ at $100 \, V$ is used in a circuit having a $200 \, V$ supply. Calculate the resistance $R$ to be connected in series with the bulb so that the power delivered by the bulb is $500 \, W$. (in $\Omega$)

Two wires of resistance $R_1$ and $R_2$ have temperature coefficients of resistance $\alpha_1$ and $\alpha_2$,respectively. These are joined in series. The effective temperature coefficient of resistance is