An ideal battery of 4 V and resistance R are connected in series in the primary circuit of a potentiometer of length 1 m and esistance 5 $$\Omega $$. The value of R, to give a potential difference of 5 mV across 10 cm of potentiometer wire, is :

A galvanometer having a resistance of 20 $$\Omega $$ and 30 divisions on both sides has figure of merit 0.005 ampere/division. The resistance that should be connected in series such that it can be used as a voltmeter upto 15 volt, is:

In the circuit shown, the potential difference between A and B is :

In the experimental set up of metre bridge shown in the figure, the null point is obtained at a distance of 40 cm from A. If a 10 $$\Omega $$ resistor is connected in series with R₁, the null point shifts by 10 cm. The resistance that should be connected in parallel with (R₁ + 10) $$\Omega $$ such that the null point shifts back to its initial position is :