$64$ 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
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Figure shows three concentric metallic spherical shells. The outermost shell has charge $q_2$, the inner most shell has charge $q_1$, and the middle shell is uncharged. The charge appearing on the inner surface of outermost shell is
Consider the combination of $2$ capacitors $C _{1}$ and $C _{2},$ with $C _{2}> C _{1},$ when connected in parallel, the equivalent capacitance is $\frac{15}{4}$ time the equivalent capacitance of the same connected in series. Calculate the ratio of capacitors, $\frac{ C _{2}}{ C _{1}}$
A $600\,pF$ capacitor is charged by $200\,V$ supply. It is then disconnected from the supply and is connected to another uncharged $600\,pF$ capacitor. Electrostatic energy lost in the process is $.........\,\mu J$.
Between the plates of a parallel plate condenser there is $1\,mm$ thick paper of dielectric constant $4$. It is charged at $100\;volt$. The electric field in $volt/metre$ between the plates of the 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......$sec$
In the circuit below $C_1=20 \,\mu F , C_2=40 \,\mu F$ and $C_3=50 \,\mu F$. If no capacitor can sustain more than $50 \,V$, then maximum potential difference between $X$ and $Y$ is .......... $V$
The capacitor of capacitance $C$ in the circuit shown is fully charged initially resistance is $R$. After the switch $S$ is closed, the time taken to reduce the stored energy in the capacitor to half its initial value is
Two insulated metallic spheres of $3\,\mu F$ and $5\,\mu F$ capacitances are charged to $300\, V$ and $500\,V$ respectively. The energy loss, when they are connected by a wire is