Electrostatic Potential and Capacitance — Class 12 Physics PYQs

In the figure curved lines represent equipotential surfaces. A charge Q is moved along different paths A, B, C and D. The work done on the charge will be maximum along the path
(A) A
(B) B
(C) C
(D) D

A circuit consisting of a capacitor C, a resistor of resistance R and an ideal battery of emf V, as shown in figure is known as RC series circuit.
As soon as the circuit is completed by closing key $S_1$ (keeping $S_2$ open) charges begin to flow between the capacitor plates and the battery terminals. The charge on the capacitor increases and consequently the potential difference $V_c$ ($=q/C$) across the capacitor also increases with time. When this potential difference equals the potential difference across the battery, the capacitor is fully charged ($Q=VC$). During this process of charging, the charge q on the capacitor changes with time t as $q=Q[1-e^{-t/RC}]$
The charging current can be obtained by differentiating it and using $\frac{d}{dx}(e^{mx})=m{e}^{mx}$.
Consider the case when R = 20 $k\Omega$, C = 500 $\mu F$ and V = 10 V.
(i) The final charge on the capacitor, when key $S_1$ is closed and $S_2$ is open, is
(A) 5 $\mu C$
(B) 5 mC
(C) 25 mC
(D) 0.1 C
(ii) For sufficient time the key $S_1$ is closed and $S_2$ is open. Now key $S_2$ is closed and $S_1$ is open. What is the final charge on the capacitor ?
(A) Zero
(B) 5 mC
(C) 2.5 mC
(D) 5 $\mu C$
(iii) The dimensional formula for RC is
(A) $[M{L}^2{T}^{-3}{A}^{-2}]$
(B) $[M^0{L}^0{T}^{-1}{A}^0]$
(C) $[M^{-1}{L}^{-2}{T}^4{A}^2]$
(D) $[M^0{L}^{0}T{A}^0]$
(iv) The key $S_1$ is closed and $S_2$ is open. The value of current in the resistor after 5 seconds, is
(A) $\frac{1}{2\sqrt{e}}$ mA
(B) $\sqrt{e}$ mA
(C) $\frac{1}{\sqrt{e}}$ mA
(D) $\frac{1}{2e}$ mA
OR
(iv) The key $S_1$ is closed and $S_2$ is open. The initial value of charging current in the resistor, is
(A) 5 mA
(B) 0.5 mA
(C) 2 mA
(D) 1 mA

A system of two conductors is placed in air and they have net charge of $+80\mu C$ and $-80\mu C$ which causes a potential difference of 16 V between them.
(1) Find the capacitance of the system.
(2) If the air between the capacitor is replaced by a dielectric medium of dielectric constant 3, what will be the potential difference between the two conductors ?
(3) If the charges on two conductors are changed to $+160\mu C$ and $-160\mu C$, will the capacitance of the system change ? Give reason for your answer.

Consider three metal spherical shells A, B and C, each of radius R. Each shell is having a concentric metal ball of radius R/10. The spherical shells A, B and C are given charges +6q, -4q, and 14q respectively. Their inner metal balls are also given charges -2q, +8q and -10q respectively. Compare the magnitude of the electric fields due to shells A, B and C at a distance 3R from their centres.

The capacitance of a parallel plate capacitor having a medium of dielectric constant K = 4 in between the plates is C. If this medium is removed, then the capacitance of the capacitor becomes :
(A) 4C
(B) C
(C) C/4
(D) 2C

Ten capacitors, each of capacitance 1 $\mu$F, are connected in parallel to a source of 100 V. The total energy stored in the system is equal to :
(A) 10${}^{-2}$ J
(B) 10${}^{-3}$ J
(C) 0.5 × 10${}^{-3}$ J
(D) 5.0 × 10${}^{-2}$ J

Three point charges Q${}_1$, Q${}_2$ and Q${}_3$ are located in x – y plane at points (– d, 0), (0, 0) and (d, 0) respectively. Q${}_1$ and Q${}_3$ are identical and Q${}_2$ is positive. What will be the nature and value of Q${}_1$ so that the potential energy of the system is zero ?

An air-filled parallel plate capacitor with plate separation 1 mm has a capacitance of 20 pF. It is charged to 4.0 $\mu$C. Calculate the amount of work done to pull its plates to a separation of 5 mm. Assume the charge on the plates remains the same.

An electric dipole consisting of charges + q and - q separated by a distance L is in stable equilibrium in a uniform electric field E. The electrostatic potential energy of the dipole is
(A) qLE
(B) zero
(C) -qLE
(D) -2qEL

The potential difference between two points in vacuum is $V_0$. If vacuum is replaced by a medium of dielectric constant K, the new value of potential difference will be __________ .