A parallel-plate capacitor is connected to a resistanceless circuit with a battery until the capacitor is fully charged. The battery is then disconnected from the circuit and the plates of the capacitor are moved to half of their original separation using insulated gloves. Let $V_{new}$ be the potential difference across the capacitor plates when the plates have moved. Let $V_{old}$ be the potential difference across the capacitor plates when they were connected to the battery $\frac{V_{new}}{V_{old}}=$......

The capacitance of a spherical condenser is $1\,\mu F$. If the spacing between the two spheres is $1\,mm$, then the radius of the outer sphere is

We have three identical metallic spheres $A, B$ and $C$. $A$ is given a charge $Q$, and $B$ and $C$ are uncharged. The following processes of touching of two spheres are carried out in succession. Each process is carried out with sufficient time.
$(i)$ $A$ and $B$      $(ii)$ $B$ and $C$
$(iii)$ $C$ and $A$      $(iv)$ $A$ and $B$
$(v)$ $B$ and $C$
The final charges on the spheres are

The magnitude of electric field $E$ in the annular region of a charged cylindrical capacitor

A $500\,\mu F$ capacitor is charged at a steady rate of $100\, \mu C/sec$. The potential difference across the capacitor will be $10\, V$ after an interval of.....$sec$

When a lamp is connected in series with capacitor, then