Electrostatic Potential and Capacitance - Bihar Board (BSEB) STD 12 Science Physics Questions

Q 1M.C.Q [1M]1 Mark

A point P is situated on the axis of an electric dipole at a distance x from its mid-point, the electric potential at point P is proportional to:

✓
$\frac{1}{x^2}$
B
$\frac{1}{x^3}$
C
$\frac{1}{x^4}$
D
$\frac{1}{x^{1 / 2}}$

Answer: A.

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Q 2M.C.Q [1M]1 Mark

The electric potential (V) inside a uniformly charged. spherical shell depends on distance:

A
$V \propto r$
✓
$V =$ constant
C
$V \propto \frac{1}{r}$
D
$V \propto \frac{1}{r^2}$

Answer: B.

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Q 3M.C.Q [1M]1 Mark

In what order should three capacitors be connected so that the energy stored in them at the same potential is maximum?

A
Two in parallel and one in series
✓
All three in parallel
C
All three in series
D
Two in series and one in parallel.

Answer: B.

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Q 4M.C.Q [1M]1 Mark

A hollow copper sphere A and a solid sphere B of equal radius are charged with the same potential. The true statement is:

A
Charge on sphere A will be more
B
Charge on sphere B will be more
✓
Both will have equal charge
D
Cannot be said with certainty.

Answer: C.

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Q 5M.C.Q [1M]1 Mark

Equal charges are located at three corners of an equilateral triangle. The true statement for electric potential V and electric field intensity E at the centre O of the triangle will be:

A
$V =0, E =0$
B
$V =0, E \neq 0$
C
$V =0, E \neq 0$
✓
$V \neq 0, E =0$

Answer: D.

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Q 61 Marks Question1 Mark

What is called equipotential surface?Draw the diagram of equipotential surface due point positive charge.

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Q 71 Marks Question1 Mark

Calculate the electric potential at a point located at a distance of $9 \times 10^{-4} m$ due to a charge of $2 \times 10^{-9} C$

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Q 81 Marks Question1 Mark

Write the value of the electric potential at the distance r from the centre of the dipole on the axis of the electric dipole of dipole moment p.

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Q 91 Marks Question1 Mark

In Millikan's experiment, $-6.4 \times 10^{-19}$ Coulomb charge is found on a charged drop, then write the number of electrons in that charged drop.

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Q 101 Marks Question1 Mark

What will be the work done in bringing a point charge from x to points y and z respectively in the given figure?

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Q 11Short Answer Type Questions [2M]2 Marks

If five capacitors $C_1, C_2, C_3, C_4, C_5$ are connected in an electric circuit as shown in the figure, then calculate the equivalent capacitance of this network between point $A$ and point $B$.

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Q 12Short Answer Type Questions [2M]2 Marks

A 12 pF capacitor is connected to a 50V battery. How much electrostatic energy is lost in the capacitor?

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Q 13Short Answer Type Questions [2M]2 Marks

Two capacitors of capacitance $3 \mu F$ and 4 $\mu F$ are charged separately from a 6 V battery. When the battery is removed, they get connected to each other. In which the negative plate of one capacitor is connected to the positive plate of the other. Calculate the total final energy.

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Q 14Short Answer Type Questions [2M]2 Marks

A parallel plate capacitor is charged with a potential difference 50 V . Thereafter it is discharged by a resistor for 2 sec , due to which its potential decreases by 10 V . Calculate the portion of energy stored in the capacitor.

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Q 15Short Answer Type Questions [2M]2 Marks

X and Y are two parallel plate capacitors, whose plates have the same area and the same distance between them. There is air between the plates of $X$ and a dielectric material of dielectric constant $k=5$ between the plates of $Y$ (in the figure). (a) Calculate the potential diffe-rence between the plates X and Y . (b) What is the ratio of electrical potential energies stored in X and Y ?

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Q 163 Marks Question3 Marks

In a parallel plate capacitor with air between the plates, each plate has an area of 6 x 10^-3m² and the distance between the plates is 3 mm. Calculate the capacitance of the capacitor. If this capacitor is connected to a 100 V supply, what is the charge on each plate of the capacitor?

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Q 173 Marks Question3 Marks

Three capacitors of capacitance 2 pF, 3 pF and 4 pF are connected in parallel.
(a) What is the total capacitance of the combination?
(b) Determine the charge on each capacitor if the combination is connected to a 100 V supply.
C₁ = 2 pF
= 2 X 10 ^-12F
C₂ = 3 pF
3 X 10 ^-12 F
C₃ = 4 pF
= 4 X 10^-12 F

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Q 183 Marks Question3 Marks

A parallel plate capacitor with air between its plates has a capacitance of 8 pF(1 pF = 10^-12F) . What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?

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Q 193 Marks Question3 Marks

Two charges 2 $\mu C$ and - 2$\mu C$ are placed at points A and B 6 cm apart.
(a) Identify an equipotential surface of the system.
(b) What is the direction of the electric field at every point on this surface?

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Q 203 Marks Question3 Marks

A regular hexagon of side 10 cm has a charge of 5 $\mu C$ at each of its vertex. Calculate the potential at the centre of the hexagon.

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Q 214 Marks Questions4 Marks

Three capacitors each of capacitance 9 pF are connected in series.
(a) What is the total capacitance of the combination?
(b) What is the potential difference across each capacitor if the combination is connected to a 120 V supply? S

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Q 224 Marks Questions4 Marks

Draw a graph showing the change in potential corresponding to the change in distance from a point charge. For the charged system shown in the figure, prove that the potential difference between points $A$ and $B$ is

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Q 23Long Answer Type Questions [5M]5 Marks

What is capacitance of a conductor? What is its unit? Find the formula for capacitance of an isolated spherical conductor. Draw a graph between capacitance and radius. If a spherical conductor is placed in dielectric constant $\in_r$, then what will be the effect on the value of capacitance?###If the area of each conducting plate of a parallel plate capacitor is A and the separation between them is $d$, then express the formula for its capacitance.

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Q 24Long Answer Type Questions [5M]5 Marks

Explain what would happn if in the capacitor given in Q. 2.8, a 3 mm thick mica sheet (of dielectric constant = 6) were inserted between the plates.
(a) while the voltage supply remained connectd.
(b) after the supply was disconncted.

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Q 25Long Answer Type Questions [5M]5 Marks

A spherical conductor of radius 12cm has a charg of $1.6 \times 10^{-7} C$ distributed uniformly on its surface. What is the electric field:
(a) inside the sphere
(b) just outside the sphere
(c) at a point 18 cm from the centre of the sphere?

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Q 26Long Answer Type Questions [5M]5 Marks

A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. How much electrostatic enery is lost in the process?

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Q 27Long Answer Type Questions [5M]5 Marks

Two charges of$5 \times 10^{-8} C$ and $-3 \times 10^{-8}$ are located at a distance of 16 cm apart. At what point on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.