A uniform wire of length 1 and radius r has a resistance of 100 $$\Omega $$. It is recast into a wire of radius $${r \over 2}.$$ The resistance of new wire will be :

A 9 V battery with internal resistance of 0.5 $$\Omega $$ is connected across an infinite network as shown in the figure. All ammeters A₁, A₂, ₃ and voltmeter V are ideal.
Choose correct statement.

A potentiometer PQ is set up to compare two resistances as shown in the figure. The ammeter A in the circuit reads 1.0 A when two way key K₃ is open. The balance point is at a length $$\ell $$₁ cm from P when two way key K₃ is plugged in between 2 and 1, while the balance point is at a length $$\ell $$₂ cm from P when key K₃ is plugged in between 3 and 1. The ratio of two resistances $${{{R_1}} \over {{R_2}}}$$, is found to be :

Which of the following statements is false?