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

Two different radioactive elements with half lives T₁ and T₂ have N₁ and N₂ undecayed atoms respectively present at a given instant. Derive an expression for the ratio of their activities at this instant in terms of N₁ and N_{2 ?}

Why is it experimentally found difficult to detect neutrinos in this process ?

A ray of light falls on a transparent sphere with centre C as shown in the figure. The ray emerges from the sphere parallel to the line AB. Find the angle of refraction at A if the refractive index of the material of the sphere is \[\sqrt{3}\].

In a parallel plate capacitor with air between the plates, each plate has an area of 6 × 10⁻³m² and the separation between the plates is 3 mm.

1. Calculate the capacitance of the capacitor.
2. If this capacitor is connected to 100 V supply, what would be the charge on each plate?
3. How would charge on the plates be affected, if a 3 mm thick mica sheet of k = 6 is inserted between the plates while the voltage supply remains connected?

Define the activity of a given radioactive substance. Write its S.I. unit.

A slab of material of dielectric constant K has the same area as that of the plates of a parallel plate capacitor but has the thickness d/2, where d is the separation between the plates. Find out the expression for its capacitance when the slab is inserted between the plates of the capacitor. 

A slab of material of dielectric constant K has the same area as that of the plates of a parallel plate capacitor but has the thickness d/3, where d is the separation between the plates. Find out the expression for its capacitance when the slab is inserted between the plates of the capacitor.

A slab of material of dielectric constant K has the same area as that of the plates of a parallel plate capacitor but has the thickness 2d/3, where d is the separation between the plates. Find out the expression for its capacitance when the slab is inserted between the plates of the capacitor.

In a given sample, two radioisotopes, A and B, are initially present in the ration of 1 : 4. The half lives of A and B are respectively 100 years and 50 years. Find the time after which the amounts of A and B become equal.

A parallel-plate capacitor is charged to a potential difference V by a dc source. The capacitor is then disconnected from the source. If the distance between the plates is doubled, state with reason how the following change:

(i) electric field between the plates

(ii) capacitance, and

(iii) energy stored in the capacitor

A radioactive nucleus ‘A’ undergoes a series of decays according to the following scheme:

The mass number and atomic number of A are 180 and 72 respectively. What are these numbers for A₄?

The radioactive isotope D decays according to the sequence

If the mass number and atomic number of D₂ are 176 and 71 respectively, what is (i) the mass number (ii) atomic number of D?

A tuning fork of frequency 480 Hz is used to vibrate a sonometer wire having natural frequency 410 Hz. The wire will vibrate with a frequency

The product of resistivity and conductivity of a cylindrical conductor depends on ____________ .

Consider a capacitor-charging circuit. Let Q₁ be the charge given to the capacitor in a time interval of 10 ms and Q₂ be the charge given in the next time interval of 10 ms. Let 10 μC charge be deposited in time interval t₁ and another 10 μC charge be deposited in the next time interval t₂.

As the temperature of a conductor increases, its resistivity and conductivity change. The ratio of resistivity to conductivity _______________ .

A parallel-plate capacitor with plate area 20 cm² and plate separation 1.0 mm is connected to a battery. The resistance of the circuit is 10 kΩ. Find the time constant of the circuit.

A parallel-plate capacitor of plate area 40 cm² and separation between the plates 0.10 mm, is connected to a battery of emf 2.0 V through a 16 Ω resistor. Find the electric field in the capacitor 10 ns after the connections are made.

A parallel-plate capacitor has plate area 20 cm², plate separation 1.0 mm and a dielectric slab of dielectric constant 5.0 filling up the space between the plates. This capacitor is joined to a battery of emf 6.0 V through a 100 kΩ resistor. Find the energy of the capacitor 8.9 μs after the connections are made.

A parallel-plate capacitor is filled with a dielectric material of resistivity ρ and dielectric constant K. The capacitor is charged and disconnected from the charging source. The capacitor is slowly discharged through the dielectric. Show that the time constant of the discharge is independent of all geometrical parameters like the plate area or separation between the plates. Find this time constant.