Science (English Medium) Class 12 - CBSE Question Bank Solutions

A resistance R is to be measured using a meter bridge. Student chooses the standard resistance S to be 100Ω. He finds the null point at l₁ = 2.9 cm. He is told to attempt to improve the accuracy. Which of the following is a useful way?

The measurement of an unknown resistance R is to be carried out using Wheatstones bridge (figure). Two students perform an experiment in two ways. The first students takes R₂ = 10 Ω and R₁ = 5 Ω. The other student takes R₂ = 1000 Ω and R₁ = 500 Ω. In the standard arm, both take R₃ = 5 Ω. Both find R = `R_2/R_1 R_3` = 10 Ω within errors.

1. The errors of measurement of the two students are the same.
2. Errors of measurement do depend on the accuracy with which R₂ and R₁ can be measured.
3. If the student uses large values of R₂ and R₁, the currents through the arms will be feeble. This will make determination of null point accurately more difficult.
4. Wheatstone bridge is a very accurate instrument and has no errors of measurement.

Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 17.7 × 10^–22 C/m². What is electric field intensity E:

1. in the outer region of the first plate, and
2. between the plates?

• Assertion (A): The given figure does not show a balanced Wheatstone bridge.
• Reason (R): For a balanced bridge small current should flow through the galvanometer.

An infinite line charge produces a field of 9 × 10⁴ N/C at a distance of 2 cm. Calculate the linear charge density.

When an AC source is connected to an ideal capacitor, show that the average power supplied by the source over a complete cycle is zero

A bulb is connected in series with a variable capacitor and an AC source as shown. What happens to the brightness of the bulb when the key is plugged in and capacitance of the capacitor is gradually reduced?

A capacitor of capacitance C is charged fully by connecting it to a battery of emf E. It is then disconnected from the battery. If the separation between the plates of the capacitor is now doubled, how will the following change?

(i) charge stored by the capacitor.

(ii) Field strength between the plates.

(iii) Energy stored by the capacitor.

Justify your answer in each case.

A capacitor of capacitance ‘C’ is charged to ‘V’ volts by a battery. After some time the battery is disconnected and the distance between the plates is doubled. Now a slab of dielectric constant, 1 < k < 2, is introduced to fill the space between the plates. How will the following be affected? (a) The electric field between the plates of the capacitor Justify your answer by writing the necessary expressions.

A capacitor of capacitance ‘C’ is charged to ‘V’ volts by a battery. After some time the battery is disconnected and the distance between the plates is doubled. Now a slab of dielectric constant, 1 < k < 2, is introduced to fill the space between the plates. How will the following be affected? (b) The energy stored in the capacitor Justify your answer by writing the necessary expressions

State and explain Gauss’s law.

Find the equivalent capacitance of the network shown in the figure, when each capacitor is of 1 μF. When the ends X and Y are connected to a 6 V battery, find out (i) the charge and (ii) the energy stored in the network.

Define capacitor reactance. Write its S.I units.

A parallel plate capacitor of capacitance C is charged to a potential V. It is then connected to another uncharged capacitor having the same capacitance. Find out the ratio of the energy stored in the combined system to that stored initially in the single capacitor.

A point charge +10 μC is a distance 5 cm directly above the centre of a square of side 10 cm, as shown in the Figure. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge 10 cm.)

Obtain the equivalent capacitance of the network in Figure. For a 300 V supply, determine the charge and voltage across each capacitor.

A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports. Show that the capacitance of a spherical capacitor is given by

C = `(4piin_0"r"_1"r"_2)/("r"_1 - "r"_2)`

where r₁ and r₂ are the radii of outer and inner spheres, respectively.

A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of 2.5 µC. The space between the concentric spheres is filled with a liquid of dielectric constant 32.

(a) Determine the capacitance of the capacitor.

(b) What is the potential of the inner sphere?

(c) Compare the capacitance of this capacitor with that of an isolated sphere of radius 12 cm. Explain why the latter is much smaller.