Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions

Two identical parallel plate capacitors A and B are connected to a battery of V volts with the switch S closed. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant K. Find the ratio of the total electrostatic energy stored in both capacitors before and after the introduction of the dielectric.

(i) Find equivalent capacitance between A and B in the combination given below. Each capacitor is of 2 µF capacitance.

(ii) If a dc source of 7 V is connected across AB, how much charge is drawn from the source and what is the energy stored in the network? 

Two identical capacitors of 12 pF each are connected in series across a battery of 50 V. How much electrostatic energy is stored in the combination? If these were connected in parallel across the same battery, how much energy will be stored in the combination now?

Also find the charge drawn from the battery in each case.

A capacitor of unknown capacitance is connected across a battery of V volts. The charge stored in it is 360 μC. When potential across the capacitor is reduced by 120 V, the charge stored in it becomes 120 μC.

Calculate:

(i) The potential V and the unknown capacitance C.

(ii) What will be the charge stored in the capacitor, if the voltage applied had increased by 120 V?

A capacitor of unknown capacitance is connected across a battery of V volts. The charge stored in it is 300 μC. When potential across the capacitor is reduced by 100 V, the charge stored in it becomes 100 μC. Calculate The potential V and the unknown capacitance. What will be the charge stored in the capacitor if the voltage applied had increased by 100 V?

A charge ‘q’ is placed at the centre of a cube of side l. What is the electric flux passing through each face of the cube?

A capacitor of capacitance ‘C’ is being charged by connecting it across a dc source along with an ammeter. Will the ammeter show a momentary deflection during the process of charging? If so, how would you explain this momentary deflection and the resulting continuity of current in the circuit? Write the expression for the current inside the capacitor.

A thin conducting spherical shell of radius R has charge Q spread uniformly over its surface. Using Gauss’s law, derive an expression for an electric field at a point outside the shell.

Draw a graph of electric field E(r) with distance r from the centre of the shell for 0 ≤ r ≤ ∞.

Three identical capacitors C₁, C₂ and C₃ of capacitance 6 μF each are connected to a 12 V battery as shown.

Find

(i) charge on each capacitor

(ii) equivalent capacitance of the network

(iii) energy stored in the network of capacitors

As `C = (1/V) Q` , can you say that the capacitance C is proportional to the charge Q?

A capacitor has capacitance C. Is this information sufficient to know what maximum charge the capacitor can contain? If yes, what is this charges? If no, what other information is needed?

A charge Q is placed at the centre of a cube. Find the flux of the electric field through the six surfaces of the cube.

A capacitor of capacitance C is charged to a potential V. The flux of the electric field through a closed surface enclosing the capacitor is

Two capacitors each having capacitance C and breakdown voltage V are joined in series. The capacitance and the breakdown voltage of the combination will be

The equivalent capacitance of the combination shown in the figure is _________ .

A thin metal plate P is inserted between the plates of a parallel-plate capacitor of capacitance C in such a way that its edges touch the two plates . The capacitance now becomes _________ .

Two metal spheres of capacitance C₁ and C₂ carry some charges. They are put in contact and then separated. The final charges Q₁ and Q₂ on them will satisfy

Three capacitors of capacitances 6 µF each are available. The minimum and maximum capacitances, which may be obtained are

The capacitance of a capacitor does not depend on