A wire of length '$$l$$' and resistance $$100 \Omega$$ is divided into 10 equal parts. The first 5 parts are connected in series while the next 5 parts are connected in parallel. The two combinations are again connected in series. The resistance of this final combination is:

Two heaters $$A$$ and $$B$$ have power rating of $$1 \mathrm{~kW}$$ and $$2 \mathrm{~kW}$$, respectively. Those two are first connected in series and then in parallel to a fixed power source. The ratio of power outputs for these two cases is:

Choose the correct circuit which can achieve the bridge balance.

A certain wire $$\mathrm{A}$$ has resistance $$81 ~\Omega$$. The resistance of another wire $$\mathrm{B}$$ of same material and equal length but of diameter thrice the diameter of A will be :