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Two capacitors of unknown capacitances C1 and C2 are connected first in series and then in parallel across a battery of 100 V. If the energy stored in the two combinations is 0.045 J and 0.25 J respectively, determine the value of C1 and C2. Also calculate the charge on each capacitor in parallel combination.
Concept: Combination of Capacitors
A capacitor 'C', a variable resistor 'R' and a bulb 'B' are connected in series to the ac mains in circuit as shown. The bulb glows with some brightness. How will the glow of the bulb change if (i) a dielectric slab is introduced between the plates of the capacitor, keeping resistance R to be the same; (ii) the resistance R is increased keeping the same capacitance?
Concept: Combination of Capacitors
Obtain the expression for the energy stored per unit volume in a charged parallel plate capacitor.
Concept: Energy Stored in a Charged Capacitor
The electric field inside a parallel plate capacitor is E. Find the amount of work done in moving a charge q over a closed loop a b c d a.
Concept: Combination of Capacitors
Derive the expression for the capacitance of a parallel plate capacitor having plate area A and plate separation d.
Concept: Capacitance of a Parallel Plate Capacitor with and Without Dielectric Medium Between the Plates
Two charged spherical conductors of radii R1 and R2 when connected by a conducting wire acquire charges q1 and q2 respectively. Find the ratio of their surface charge densities in terms of their radii.
Concept: Conductors and Insulators Related to Electric Field
Considering the case of a parallel plate capacitor being charged, show how one is required to generalize Ampere's circuital law to include the term due to displacement current.
Concept: The Parallel Plate Capacitor
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.
Concept: Capacitors and Capacitance
Find out the amount of the work done to separate the charges at infinite distance.
Concept: Potential Energy of a System of Charges
What is the geometrical shape of equipotential surfaces due to a single isolated charge?
Concept: Equipotential Surfaces
In the given circuit diagram a voltmeter ‘V’ is connected across a lamp ‘L’. Ho would (i) the brightness of the lamp and (ii) voltmeter reading ‘V’ be affected, if the value of resistance ‘R’ is decreased? Justify your answer.
Concept: Effect of Dielectric on Capacity
A capacitor, made of two parallel plates each of plate area A and separation d, is being charged by an external ac source. Show that the displacement current inside the capacitor is the same as the current charging the capacitor.
Concept: Capacitance of a Parallel Plate Capacitor with and Without Dielectric Medium Between the Plates
Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero.
Concept: Equipotential Surfaces
Draw a plot showing the variation of (i) electric field (E) and (ii) electric potential (V) with distance r due to a point charge Q.
Concept: Electric Potential
- Assertion (A): Work done in moving a charge around a closed path, in an electric field is always zero.
- Reason (R): Electrostatic force is a conservative force.
Concept: Potential Energy of a System of Charges
Justify your answers for each case.
State the significance of the negative value of electrostatic potential energy of a system of charges.
Three charges are placed at the corners of an equilateral triangle ABC of side 2.0 m as shown in the figure. Calculate the electric potential energy of the system of three charges.
Concept: Potential Energy of a System of Charges
The capacitors, each of 4 µF are to be connected in such a way that the effective capacitance of the combination is 6 µF. This can be achieved by connecting ______.
Concept: Combination of Capacitors
Read the following paragraph and answer the questions.
| A capacitor is a system of two conductors separated by an insulator. The two conductors have equal and opposite charges with a potential difference between them. The capacitance of a capacitor depends on the geometrical configuration (shape, size and separation) of the system and also on the nature of the insulator separating the two conductors. They are used to store charges. Like resistors, capacitors can be arranged in series or parallel or a combination of both to obtain the desired value of capacitance. |
- Find the equivalent capacitance between points A and B in the given diagram.
- A dielectric slab is inserted between the plates of the parallel plate capacitor. The electric field between the plates decreases. Explain.
- A capacitor A of capacitance C, having charge Q is connected across another uncharged capacitor B of capacitance 2C. Find an expression for (a) the potential difference across the combination and (b) the charge lost by capacitor A.
OR
Two slabs of dielectric constants 2K and K fill the space between the plates of a parallel plate capacitor of plate area A and plate separation d as shown in the figure. Find an expression for the capacitance of the system.
Concept: Capacitors and Capacitance
Graph showing the variation of current versus voltage for a material Ga As is shown in the figure. Identify the region of
(i) negative resistance
(ii) where Ohm's law is obeyed.
Concept: Ohm's Law
Use Kirchhoff's rules to obtain conditions for the balance condition in a Wheatstone bridge.
Concept: Kirchhoff’s Laws
