Electrostatic Potential and Capacitance

An 8 µF capacitor is connected across 200 V, 50 Hz line.  What is the peak value of the charge through capacitor?

• 2.5 x 10^-3 C

• 2.5 x 10^-4 C

• 5 x 10^-5 C

• 7.5 x 10^-2 C

A conducting sphere ofradius 30 cm is given a charge of 1.2 x 10^-8 C. What will be its potential ?

• 0.03 kV

• 0.9 kV

• 1.8 kV

• 3.6 kV

Capacitance of a parallel plate capacitor becomes $\frac{3}{2}$ times its original value if a dielectric slab of thickness $\frac{\mathrm{d}}{2}$ is inserted between the plates, where d is the separation between the plates. The dielectric constant of the slab is

• 4

• 2

• 3

• 1

The electric potential V at any point x, y, z in space is given by V = 4 x² . The electric field at the point (2, 0, 1) in Vm^-1 is

• 10 $\stackrel{\wedge }{\mathrm{j}}$

• 20 $\stackrel{\wedge }{\mathrm{j}}$

• − 16 $\stackrel{\wedge }{\mathrm{i}}$

• 30 $\stackrel{\wedge }{\mathrm{i}}$

A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be

• 400 %

• 66.6 %

• 33.3 %

• 200 %

In the circuit, shown in figure, K is open. The charge on capacitor C in steady state is q. Now, key is closed and at steady state, the charge on C is q₂ the ratio of charges $\left(\frac{{\mathrm{q}}_1}{{\mathrm{q}}_2}\right)$ is 

• $\frac{3}{2}$

• $\frac{2}{3}$

• 1

• $\frac{1}{2}$

A long hollow conducting cylinder is kept co-axially inside  another long and hollow conducting cylinder of larger  radius. Both the cylinders are initially electrically neutral.Now consider the following statements

1. A potential difference appears between the two cylinders when a charge density is given to the inner cylinder.
2. A potential difference appears between the two cylinders when a charge density is given to the outer cylinder.
3. No potential difference appears between the two cylinders when a uniform line
   charge is kept along the axis of cylinders.
4. No potential difference appears between the two cylinders when same charge
   density is given to both the cylinders.

Which of the above mentioned statement is/are correct?

• Only I

• I, IV

• Only II

• Only III

In a region, the potential is represented by V (x,y,z) = 6x − 8xy − 8y + 6yz where V is in volts and x,y,z are in meters. The electric force experienced by a charge of 2C situated at point (1,1,1) is

• $6\sqrt{5} \mathrm{N}$

• 30 N

• 24 N

• $4\sqrt{35} \mathrm{N}$

Two charges q and -3q are placed fixed on X-axis separated by distance d. Where should a third charge 2q be placed such that it will not experience any force?

• $\frac{\sqrt{3} + 2\mathrm{d}}{2}$

• $\frac{\sqrt{3} + 2\mathrm{d}}{3}$

• $\frac{\mathrm{d} + \sqrt{3} \mathrm{d}}{2}$

• $\frac{\sqrt{3} \mathrm{d}}{2}$

In the shown figure, what is the potential difference between the points A and B and between B and C respectively in steady state ? 

• V_AB = V_BC = 100 V

• V_AB = 75 V , V_BC = 25 V

• V_AB = 25 V , V_BC = 75 V

• V_AB = V_BC = 50 V