The current drawn from the battery in the given network is (Internal resistance of the battery is negligible)

Rails of material of steel are laid with gaps to allow for thermal expansion. Each track is 10 m long, when laid at temperature $17^{\circ} \mathrm{C}$. The maximum temperature that can be reached is $45^{\circ} \mathrm{C}$. The gap to be kept between the two segments of railway track is

$$\left(\alpha_{\text {steel }}=1.3 \times 10^{-5} /{ }^{\circ} \mathrm{C}\right)$$

If the potential difference used to accelerate electrons is doubled. By what factor does the deBroglie wavelength $(\lambda)$ associated with the electrons change?

In an adiabatic process for an ideal gas, the relation between the universal gas constant ' $R$ ' and specific heat at constant volume ' $\mathrm{C}_{\mathrm{v}}$ ' is $R=0.4 C_v$. The pressure ' $P$ ' of the gas is proportional to the temperature ' $T$ ', of the gas as $T^k$. The value of constant ' K ' is