In the circuit shown here ${C_1} = 6\,\mu F,\;{C_2} = 3\,\mu F$ and battery $B = 20\,V$. The switch ${S_1}$ is first closed. It is then opened and afterwards ${S_2}$ is closed. What is the charge finally on ${C_2}$.......$\mu C$
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A molecule with a dipole moment $p$ is placed in an electric field of strength $E$. Initially the dipole is aligned parallel to the field. If the dipole is to be rotated to be anti-parallel to the field, the work required to be done by an external agent is
A capacitor of $2\,\, \mu F$ is charged as shown in the diagram. When the switch $S$ is turned to position $2,$ the percentage of its stored energy dissipated is ......$\%$
Two capacitors of capacitances $1\ \mu F$ and $3\ \mu F$ are charged to the same voltages $5\,V$. They are connected in parallel with oppositely charged plates connected together. Then:
If $3$ charges are placed at the vertices of equilateral triangle of charge ‘$q$’ each. What is the net potential energy, if the side of equilateral triangle is $l\, cm$
Two identical positive charges are placed on the $y$-axis at $y=-a$ and $y=+a$. The variation of $V$ (electric potential) along $x$-axis is shown by graph
An infinitely long thin wire, having a uniform charge density per unit length of $5 nC / m$, is passing through a spherical shell of radius $1 m$, as shown in the figure. A $10 nC$ charge is distributed uniformly over the spherical shell. If the configuration of the charges remains static, the magnitude of the potential difference between points $P$ and $R$, in Volt, is. . . .
[Given: In SI units $\frac{1}{4 \pi \in_0}=9 \times 10^9, \ln 2=0.7$. Ignore the area pierced by the wire.]
An electric dipole of moment $p$ is placed in an electric field of intensity $E.$ The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $\theta = 90^o$ , the torque and the potential energy of the dipole will respectively be