Electric potential and capacitance practice · Mixed difficulty

The ratio of the resultant capacities when three capacitors of $2\,\,\mu F,\,\,4\,\,\mu F$ and $6\,\,\mu F$ are connected first in series and then in parallel is

Three condensers each of capacitance $2F$ are put in series. The resultant capacitance is

A 20 F capacitor is charged to 5 V and isolated. It is then connected in parallel with an uncharged 30 F capacitor the decrease in the energy of the system will be

Assertion (A): In the electric field $\mathbf{E}=(4 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}) \mathrm{N} / \mathrm{C}$, electric potential at $A(4 \mathrm{~m}, 0)$ is more than the electric potential at $B(0,4 \mathrm{~m})$.

Reason (R): Electric lines of forces always travel from higher potential to lower potential.

Statement-I: The potential at any point due to a group of '$N$' point charges is simply arrived at by the principle of superposition.
Statement-II: The potential energy of a system of two charges is a scalar quantity.

Two particles of identical mass are moving in circular orbits under a potential given by $V(r)=K r^{-n},$ where $K$ is a constant. If the radii of their orbits are $r_1 \cdot r_2$ and their speeds are $v_1 \cdot v_2$, respectively. Then

Two condensers of capacities $1\mu F$ and $2\mu F$ are connected in series and the system is charged to $120\;volts.$ Then the P.D. on $1\mu F$ capacitor (in volts) will be

A point Q lies on the perpendicular bisector of an electrical dipole of dipole moment p. If the distance of Q from the dipole is r (much larger than the size of the dipole), then the electric intensity E at Q is proportional to

If in a parallel plate capacitor, which is conected to a battery, we fill dielectrics in whole space of its plates, then which of the following increases?

Two charges of each magnitude $0.01 \mathrm{C}$ and separated by a distance of $0.4 \mathrm{mm}$ constitute an electric dipole. If the dipole is placed in an uniform electric field '$\vec{E}$' of 10 dyne/C making $30^{\circ}$ angle with $\vec{E}$, the magnitude of torque acting on dipole is:

There are four concentric shells $A, B, C$ and $D$ of radii $a, 2 a, 3 a$ and $4 a$ respectively. Shells $B$ and $D$ are given charges $+q$ and $-q$ respectively. Shell $C$ is now earthed. The potential difference $V_A-V_C$ is $\left(k=\frac{1}{4 \pi \varepsilon_0}\right)$

Two capacitors of capacities $C_1$ and $C_2$ are charged up to the potential $V_1$ and $V_2$ then condition for not flowing the charge between on connected them in parallel is

Two hollow conducting spheres of radii ${R_1}$ and ${R_2}({R_1} > > {R_2})$ have equal charges. The potential would be:

A spherical equipotential surface is not possible

A parallel plate capacitor of capacity ${C_0}$ is charged to a potential ${V_0}$ (i) The energy stored in the capacitor when the battery is disconnected and the separation is doubled ${E_1}$ (ii) The energy stored in the capacitor when the charging battery is kept connected and the separation between the capacitor plates is doubled is ${E_2}.$ Then ${E_1}/{E_2}$ value is

In a certain charge distribution, all points having zero potential can be joined by a circle $\mathrm{S}$. Points inside $\mathrm{S}$ have positive potential, and points outside $\mathrm{S}$ have negative potential. A positive charge, which is free to move, is placed inside $\mathrm{S}$:

Two capacitors of capacitances $3 \mu \mathrm{F}$ and $6 \mu \mathrm{F}$, are charged to potentials of $2 \mathrm{~V}$ and $5 \mathrm{~V}$ respectively. These two charged capacitors are connected in series. Find the potential across each of the two capacitors now.