If half of the space between the plates of a parallel plate capacitor is filled with a medium of dielectric constant 4 , the capacitance is $C_1$. If one-third of the space between the plates of the capacitor is filled with the medium of dielectric constant 4 , the capacitance is $C_2$. If in both cases, the dielectric is placed parallel to the plated of the capacitor, then $C_1: C_2=$

The potential difference between the ends of a straight conductor of length 20 cm is 16 V . If the drift speed of the electrons is $2.4 \times 10^{-4} \mathrm{~ms}^{-1}$, the electron mobility in $\mathrm{m}^2 \mathrm{~V}^{-1} \mathrm{~s}^{-1}$ is

The potential difference $V$ across the filament of the bulb shown in the given Wheatstone bridge varies as $V=i(2 i+1)$, where $i$ is the current in ampere through the filament of the bulb. The emf of the battery $V_a$, so that the bridge become balanced is

Two points $A$ and $B$ on the axis of a circular current loop are at distances of 4 cm and $3 \sqrt{3} \mathrm{~cm}$ from the centre of the loop. If the ratio of the induced magnetic fields at points $A$ and $B$ is $216: 125$, then radius of the loop is