An infinite sequence of resistors is shown in the figure. The resultant resistance between $A$ and $B$ will be,when $R_1 = 1\,\Omega$ and $R_2 = 2\,\Omega$ ............. $\Omega$

The emf of a cell of internal resistance $2 \ \Omega$ is measured using a voltmeter of resistance $998 \ \Omega$. The error in the emf measured is (in $\%$)

The figure shows three circuits $I, II$ and $III$ which are connected to a $3\,V$ battery. If the powers dissipated by the configurations $I, II$ and $III$ are $P_1, P_2$ and $P_3$ respectively,then

An electrical circuit consists of ten $100 \,\Omega$ resistors. Out of these $10$ resistors,a group of $n_1$ resistors are connected in parallel and another group of $n_2$ resistors are separately connected in parallel. These two groups are then connected in series and this combination is connected to a voltage source of $100 \,V$. If the net current through the circuit is $2.5 \,A$,the values of $n_1$ and $n_2$ are:

In the circuit given below,if the bulb is to glow with maximum intensity,the value of $R$ is (neglect internal resistance of the cell) (in $Omega$)

Six resistors of $3 \; \Omega$ each are connected along the sides of a hexagon and three resistors of $6 \; \Omega$ each are connected along $AC$, $AD$, and $AE$ as shown in the figure. The equivalent resistance between $A$ and $B$ is equal to