List of top Physics Questions on electrostatic potential and capacitance

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). 
Assertion (A): Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain. 
Reason (R): Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa. In the light of the above statements, choose the most appropriate answer from the options given below:

A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is:

Arrange the following in the ascending order of wavelength (\( \lambda \)): 
(A) Microwaves (\( \lambda_1 \)) 
(B) Ultraviolet rays (\( \lambda_2 \)) 
(C) Infrared rays (\( \lambda_3 \)) 
(D) X-rays (\( \lambda_4 \)) 
Choose the most appropriate answer from the options given below:

A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is:
Two capacitors \( C_1 \) and \( C_2 \) are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are \( U_1 \) and \( U_2 \), respectively. Which of the given statements is true?
Two capacitors C1 and C2 are connected in parallel to a battery
Three infinitely long wires with linear charge density \( \lambda \) are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface?

The output of the circuit is low (zero) for:

(A) \( X = 0, Y = 0 \) 
(B) \( X = 0, Y = 1 \) 
(C) \( X = 1, Y = 0 \) 
(D) \( X = 1, Y = 1 \) 
Choose the correct answer from the options given below:

In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of \( P_1 \) and \( P_2 \) are orthogonal to each other. The polarizer \( P_3 \) covers both the slits with its transmission axis at \( 45^\circ \) to those of \( P_1 \) and \( P_2 \). An unpolarized light of wavelength \( \lambda \) and intensity \( I_0 \) is incident on \( P_1 \) and \( P_2 \). The intensity at a point after \( P_3 \), where the path difference between the light waves from \( S_1 \) and \( S_2 \) is \( \frac{\lambda}{3} \), is: 

The charge on a parallel plate capacitor is 200 μC and its capacitance is 4 μF. If the distance between the plates of the capacitor is 2 mm, then the electric force between the plates of the capacitor is
If a charge of 3 nC is placed at each vertex of a cube of side 3 m, then the electric potential at the centre of the cube is:
A thin pencil of length \( f/4 \) is placed coinciding with the principal axis of a mirror of focal length \( f \). The image of the pencil is real and enlarged, just touches the pencil. Calculate the magnification produced by the mirror.
With the help of given circuit, find out:
(i) Equivalent capacity of the combination
(ii) Charge on capacitor \(c_1\)
(iii) Total stored energy of the combination.}
\includegraphics[width=0.5\linewidth]{image6.png}
What is the meaning of electrical capacity of a conductor? Find the unit of the electrical capacity of the conductor.
Do two equipotential surfaces intersect each other? Answer with reason.
What is an electrical capacitor? Find the expression for the capacity of a parallel plate capacitor. On which factors does the capacitance depend?
Four capacitors of equal capacity are connected in series with a battery of 20 V. The middle point O is earthed. Calculate the potential at points P and Q. \includegraphics[width=0.5\linewidth]{image3.png}
What is meant by the electric potential energy of the system of point charges? Compute the total electric potential energy of the system of charges given in the figure.
\includegraphics[width=0.5\linewidth]{image6.png}
Write down the formula and unit of surface charge density. A charge \( Q \) is distributed over two concentric hollow spheres of radii \( r_1 \) and \( r_2 (r_1 > r_2) \). If their surface charge densities are equal, find the electric potential at their common centre.
Find out the equivalent capacitance and total energy stored in the given combination of capacitors:
\includegraphics[width=0.5\linewidth]{image3.png}
Deduce the equation of potential energy of a charged condenser and show that the energy density in the electric field between the plates of charged condenser is \(\frac{1}{2} \epsilon_0 E^2\).
Show that \(\frac{\text{Farad}}{\text{meter}} = \frac{\text{coulomb}^2}{\text{newton} \times \text{meter}^2}\). Name its physical quantity. If potential difference across ends of capacitor of capacitance 6 \(\mu\)F is 2 volts, find out the potential difference across ends of the battery :
\begin{center} \begin{circuitikz} \draw (0,2) to[C, l=4F] (2,2) to[C, l=6F] (4,2); \draw (4,2) -- (4,0); \draw (4,0) to[battery1, l=V] (0,0); \draw (0,0) -- (0,2); \end{circuitikz} \end{center}
Obtain the expression for capacity of a parallel plate capacitor. How the capacity will be increased?
Light consisting of two wavelengths 600 nm and 480 nm is used to obtain interference fringes in a double slit experiment. The screen is placed 1.0 m away from slits which are 1.0 mm apart. (i) Calculate the distance of the third bright fringe on the screen from the central maximum for wavelength 600 nm.
A ray of light is incident on a refracting face AB of a prism ABC at an angle of \( 45^\circ \). The ray emerges from face AC and the angle of deviation is \( 15^\circ \). The angle of prism is \( 30^\circ \). Show that the emergent ray is normal to the face AC from which it emerges out. Find the refraction index of the material of the prism.
The electric field at a point in space is \( 2 \times 10^3 \, \text{N/C} \) and the potential at the same point is \( 100 \, \text{V} \). What is the potential energy of a charge of \( 5 \, \mu\text{C} \) placed at that point?