Two electric dipoles of moment $P$ and $8P$ are placed in opposite directions on a line at a distance of $24$ cm. The electric field will be zero at the point between the dipoles whose distance from the dipole of moment $P$ will be $x_1$. When $8P$ is replaced by $27P$ keeping all other quantities the same, the distance $x_1$ now becomes $x_2$. The difference $|x_2 - x_1|$ is ( All the distances are measured from the centers of the dipole.)

A parallel plate capacitor of capacitance 'C' is connected to a battery and charged to a potential 'V'. Another capacitor of capacitance '$3C$' is charged to a potential '$3V$'. The charging battery is then disconnected and both the capacitors are connected in parallel to each other such that positive terminal of one is connected to negative terminal of the other. The final energy of the configuration is

A slab of material of dielectric constant $K$ has the same area as the plates of a parallel plate capacitor but has a thickness $(4/5)d$, where $d$ is the separation of the plates. The capacitance in the presence and absence of dielectric are $C$ and $C_0$ respectively. The ratio $(C/C_0)$ is

In a meter bridge experiment, the balance point is obtained at length '$l_1$' cm from left hand when resistances in the left gap and right gap are $15 \ \Omega$ and $R \ \Omega$ respectively. When the resistance $R$ is shunted with equal resistance the new balance point is at $(1.6\,l_1)$. The resistance $R$ in ohm is