A meter bridge is set up as shown, to determine an unknown resistance X using a standard 10 $$\Omega$$ resistor. The galvanometer shows null point when tapping-key is at 52 cm mark. The end-corrections are 1 cm and 2 cm, respectively, for the ends A and B. The determined value of X is

Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, 100, 60 and 40 W bulbs have filament resistances R₁₀₀, R₆₀ and R₄₀ respectively, the relation between these resistances is

To verify Ohm's law, a student is provided with a test resitor R_T, a high resistance R₁, a small resistance R₂, two identical galvanometers G₁ and G₂, and a variable voltage source V. The correct circuit to carry out the experiment is

Consider a thin square sheet of side L and thickness, made of a material of resistivity $$\rho$$. The resistance between two opposite faces, shown by the shaded areas in the figure is