A capacitor $C = 100$ $ \mu F$ is connected to three resistor each of resistance $1$ $k\Omega$ and a battery of $emf$ $9\,V$. The switch $S$ has been closed for long time so as to charge the capacitor. When switch $S$ is opened, the capacitor discharges with time constant......$ms$
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$64$ small drops of mercury, each of radius $ r$ and charge $q$ coalesce to form a big drop. The ratio of the surface density of charge of each small drop with that of the big drop is
The adjacent diagram shows a charge $+Q$ held on an insulating support $S$ and enclosed by a hollow spherical conductor. $O$ represents the centre of the spherical conductor. and $P$ is a point such that $OP = x $ and $SP = r$ . The electric field at point $P$ will be
Effective capacitance of parallel combination of two capacitors $\mathrm{C}_{1}$ and $\mathrm{C}_{2}$ is $10\; \mu \mathrm{F}$. When these capacitors are individually connected to a voltage source of $1\; \mathrm{V},$ the energy stored in the capacitor $\mathrm{C}_{2}$ is $4$ times that of $\mathrm{C}_{1}$. If these capacitors are connected in series, their effective capacitance will be
In a certain reglon of space with volume $0.2\, m ^{3}$ the electric potential is found to be $5\, V$ throughout. The magnitude of electric field in this region is ______ $N/C$
Two parallel plate capacitor with different plate seperation but the same capacitance are connected in series to a battery. Both capacitors are filled with air. The quantity that is $NOT$ the same for both the capacitors when they are fully charged is
A neutral spherical copper particle has a radius of $10 \,nm \left(1 \,nm =10^{-9} \,m \right)$. It gets charged by applying the voltage slowly adding one electron at a time. Then, the graph of the total charge on the particle versus the applied voltage would look like
The plates of a parallel plate capacitor with no dielectric are connected to a voltage source. Now a dielectric of dielectric constant $K $ is inserted to fill the whole space between the plates with voltage source remaining connected to the capacitor.
A parallel plate capacitor is made of two square plates of side $a$, separated by a distance $d\,(d < < a)$. The lower triangular portion is filled with a dielectric of dielectric constant $K$, as shown in the figure. Capacitance of this capacitor is
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.....$sec$