A capacitor is a system of two conductors separated

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Case Study Chapter 2 Electrostatic Potential and Capacitance :

A capacitor is a system of two conductors separated

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 desired value of capacitance.                                    [CBSE  2023]

(i) Find the equivalent capacitance between points A and B in the given diagram.                     (1)

A capacitor is a system of two conductors separated

(ii) A dielectric slab is inserted between the plates of a parallel plate capacitor. The electric field between the plates decreases, Explain.                      (1)

(iii) 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.                                 (2)

OR

(iii) 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 as shown in figure. Find an expression for capacitance of the system.                      (2)

A capacitor is a system of two conductors separated

Solution :

A capacitor is a system of two conductors separated

(i)  \therefore \dfrac{1}{C_{eq}} = \dfrac{1}{C_1} + \dfrac{1}{C_2}

= \dfrac{1}{C} + \dfrac{1}{C}= \dfrac{2}{C}

\Rightarrow C_{eq} = \dfrac{C}{2}

A capacitor is a system of two conductors separated

C_{net} = C_1 + C_2 + C_3

\Rightarrow C_{net} = \dfrac{C}{2} + \dfrac{C}{2} + C

\Rightarrow C_{net} = 2C

Total capacitance between AB = 2C

(ii) When a dielectric is inserted between the plates of a capacitor, the electric field decrease. This is due to polarisation of the charge within the dielectric, which results in induced surface charges. Capacitor is greater by a factor K, where K is the dielectric constant of the material.

(iii) (a) Potential, V = \dfrac{Q+0}{C + 2C} = \dfrac{Q}{3C}

(b) Charge lost by capacitor A = Q/3.

OR

(iii) We know that,

C = \dfrac{K\epsilon_0 A}{d}

\therefore C_1 = \dfrac{2K\epsilon_0 A}{d/3} = \dfrac{6K\epsilon_0 A}{d}

\therefore C_2 = \dfrac{K\epsilon_0 A}{2d/3} = \dfrac{3K\epsilon_0 A}{2d}

Now, the effective capacitance for series combination,

\dfrac{1}{C_{eq}} = \dfrac{1}{C_1} + \dfrac{1}{C_2}

\Rightarrow C_{eq} = \dfrac{C_1C_2}{C_1 + C_2}

= \dfrac{\dfrac{6K\epsilon_0 A}{d}.\dfrac{3K\epsilon_0 A}{2d}}{\dfrac{6K\epsilon_0 A}{d} + \dfrac{3K\epsilon_0 A}{2d}}

= \dfrac{\dfrac{6K\epsilon_0 A}{d}.\dfrac{3K\epsilon_0 A}{2d}}{\dfrac{15}{2}.\dfrac{K\epsilon_0 A}{2d}}

= \dfrac{6}{5}.\dfrac{K\epsilon_0 A}{d}

Case Study Chapter 5 : Magnetism and Matter

Read the following paragraph and answer the questions :

Consider the experimental set up shown in the figure . This jumping ring expriment is an outstanding demostration of some simple laws of physics. A conducting non-magnetic ring is placed over the verticle core of a solenoid. When current is passed through the solenoid. The ring is thrown off.              [CBSE   2023]

Solution: See solution

Case Study Physics Chapter 3 – Current Electricity

Read the following paragraph and answer the question.

When Deepak studies the electrical circuits and the current flowing through them, he became curious about the range of the currents we come across in daily life. He collected the data and presented in a tabular form as shown below. He then studied the instruments used to detect and measure current, however could not understand the difference between an ammeter and an ideal ammeter and thus went to this teacher for the explanation.

Solution: See full solution

Case Study

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