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A capacitor is connected to a $20\, {V}$ battery through a resistance of $10\, \Omega .$ It is found that the potential difference across the capacitor rises to $2\, {V}$ in $1\, \mu {s}$. The capacitance of the capacitor is $....\,\mu {F}$ Given : $\ln \left(\frac{10}{9}\right)=0.105$
A metallic spherical shell has an inner radius $R_1$ and outer radius $R_2$. A charge $Q$ is placed at the centre of the spherical cavity. What will be surface charge density on the inner surface
Three capacitors $C_1,\,C_2$ and $C_3$ are connected as shown in the figure to a battery of $V\,volt$. If the capacitor $C_3$ breaks down electrically the change in total charge on the combination of capacitors is
A parallel plate capacitor of area ' $A$ ' plate separation ' $d$ ' is filled with two dielectrics as shown. What is the capacitance of the arrangement?
Two condensers of capacity $0.3\,\mu F$ and $0.6\,\mu F$ respectively are connected in series. The combination is connected across a potential of $6\,volts$. The ratio of energies stored by the condensers will be
There is a uniform spherically symmetric surface charge density at a distance $R_0$ from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed $V(R(t))$ of the distribution as a function of its instantaneous radius $R(t)$ is
Four plates of the same area of cross-section are joined as shown in the figure. The distance between each plate is $d$. The equivalent capacity across $A$ and $B$ will be
The plates of a capacitor are charged to potential difference of $V\, volts$ and then connected across a resistor. The potential difference across the capacitor decreases exponentially with respect to time. After one second, the potential difference between the plates is $V/3$; then after two seconds from the start, the potential difference between the plates is