An infinite ladder network is arranged with resistances $R$ and $2R$ as shown. The effective resistance between terminals $A$ and $B$ is

Two resistances $R_1$ and $R_2$ are made of different materials. The temperature coefficient of the material of $R_1$ is $\alpha$ and of the material of $R_2$ is $-\beta$. The resistance of the series combination of $R_1$ and $R_2$ will not change with temperature,if $R_1/R_2$ equals

When connected across the terminals of a cell,a voltmeter measures $5\,V$ and a connected ammeter measures $10\,A$ of current. $A$ resistance of $2\,\Omega$ is connected across the terminals of the cell. The current flowing through this resistance will be ............ $A$.

$A$ battery of $e.m.f.$ $E$ and internal resistance $r$ is connected to a variable resistor $R$ as shown in the figure. Which one of the following is true?

Find the current in the $3\,\Omega$ resistance in the given circuit.

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