The value of unknown resistance $$(x)$$ for which the potential difference between $$B$$ and $$D$$ will be zero in the arrangement shown, is :

The ratio of heat dissipated per second through the resistance $$5 \Omega$$ and $$10 \Omega$$ in the circuit given below is:

A galvanometer of resistance $$100 \Omega$$ when connected in series with $$400 \Omega$$ measures a voltage of upto $$10 \mathrm{~V}$$. The value of resistance required to convert the galvanometer into ammeter to read upto $$10 \mathrm{~A}$$ is $$x \times 10^{-2} \Omega$$. The value of $$x$$ is :

In the given figure $$\mathrm{R}_1=10 \Omega, \mathrm{R}_2=8 \Omega, \mathrm{R}_3=4 \Omega$$ and $$\mathrm{R}_4=8 \Omega$$. Battery is ideal with emf $$12 \mathrm{~V}$$. Equivalent resistant of the circuit and current supplied by battery are respectively :