Four capacitors of each of capacity $3\,\mu F$ are connected as shown in the adjoining figure. The ratio of equivalent capacitance between $A$ and $B$ and between $A$ and $C$ will be
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Twenty seven drops of water of the same size are equally and similarly charged. They are then united to form a bigger drop. By what factor will the electrical potential changes.........$times$
Electric charges of $ + 10\,\mu C,\; + 5\,\mu C,\; - 3\,\mu C$ and $ + 8\,\mu C$ are placed at the corners of a square of side $\sqrt 2 \,m$. the potential at the centre of the square is
A parallel plate capacitor of capacitance $C$ is connected to a battery and is charged to a potential difference $V$. Another capacitor of capacitance $2C$ is similarly charged to a potential difference $2V$. The charging battery is now disconnected and the capacitors are connect in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is
A capacitor of capacity $C$ is charged to a steady potential difference $V$ and connected in series with an open key and a pure resistor $'R'$. At time $t = 0$, the key is closed. If $I =$ current at time $t$, a plot of log $I$ against $'t'$ is as shown in $(1)$ in the graph. Later one of the parameters i.e. $V, R$ or $C$ is changed keeping the other two constant, and the graph $(2)$ is recorded. Then
There exists a uniform electric field $E=4 \times 10^5 \,Vm ^{-1}$ directed along negative $x$-axis such that electric potential at origin is zero. Acharge of $-200 \,\mu C$ is placed at origin, and a charge of $+200 \,\mu C$ is placed at $(3 \,m , 0)$. The electrostatic potential energy of the system is ...........$J$
A spherical drop of mercury having a potential of $2.5\, V$ is obtained as a result of merging $125$ droplets. The potential of constituent droplets would be........$V$
A non-conducting ring of radius $0.5\,m$ carries a total charge of $1.11 \times {10^{ - 10}}\,C$ distributed non-uniformly on its circumference producing an electric field $\vec E$ everywhere in space. The value of the line integral $\int_{l = \infty }^{l = 0} {\, - \overrightarrow E .\overrightarrow {dl} } \,(l = 0$ being centre of the ring) in volt is
Consider a thin spherical shell of radius $R$ with its centre at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field $|\vec{E}(r)|$ and the electric potential $V(r)$ with the distance r from the centre, is best represented by which graph?
An electric dipole of dipole moment is $6.0 \times 10^{-6}\,Cm$ placed in a uniform electric field of $1.5 \times 10^3\,NC ^{-1}$ in such a way that dipole moment is along electric field. The work done in rotating dipole by $180^{\circ}$ in this field will be $.........\,mJ$