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Physics

Electrostatic Potential and Capacitance

Effect of dielectric in capacitors

The equivalent capacitance of the arrangement shown in figure,

Question

Easy

Solving time: 2 mins

The equivalent capacitance of the arrangement shown in figure, if $A$ is the area of each plate, is

C = \frac{ε _{0} A}{d} [\frac{K _{1}}{2} + \frac{K _{2} + K _{3}}{K _{2} K _{3}}]

C = \frac{ε _{0} A}{d} [\frac{K _{1}}{2} + \frac{K _{2} K _{3}}{K _{2} + K _{3}}]

C = \frac{ε _{0} A}{2 d} [K_{1} + \frac{K _{2} K _{3}}{K _{2} + K _{3}}]

C = \frac{ε _{0} A}{d} [K_{1} + \frac{K _{2} K _{3}}{K _{2} + K _{3}}]

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Electricity and Magnetism (DC Pandey)

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The equivalent capacitance of the arrangement shown in figure, if

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Text solutionVerified

C = C_{LHS} + C_{RHS}

= \frac{K _{1} ε _{0} ( A /2 )}{d} + \frac{ε _{0} ( A /2 )}{d - d /2 - d /2 + \frac{d /2}{K _{2}} + \frac{d /2}{K _{3}}}

= \frac{ε _{0} A}{d} [\frac{K _{1}}{2} + \frac{K _{2} K _{3}}{K _{2} + K _{3}}]

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Practice questions from Electricity and Magnetism (DC Pandey)

Question 1

Hard

A capacitor of capacitance

C

has a potential difference

E /2

and another capacitor of capacitance

2 C

is uncharged. They are joined to form a closed circuit as shown in the figure.
(a) Find the current in the circuit at

t = 0

.
(b) Find the charge on

C

as a function of time.

Topic:

Electrostatic Potential and Capacitance

Book:

Electricity and Magnetism (DC Pandey)

View 2 solutions

Question 2

Medium

The figure shows a graph of the current in a discharging circuit of a capacitor through a resistor of resistance

10Ω

The initial potential difference across the capacitor is $100 V$
The capacitance of the capacitor is $\frac{1}{10 l n 2} F$
The total heat produced in the circuit will be $\frac{500}{l n 2} J$
All of the above

Topic:

Electrostatic Potential and Capacitance

Book:

Electricity and Magnetism (DC Pandey)

View 4 solutions

Question 3

Medium

Three parallel metallic plates each of area A are kept as shown in figure and charges

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Topic:

Electrostatic Potential and Capacitance

Book:

Electricity and Magnetism (DC Pandey)

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Question 4

Hard

A capacitor of capacitance

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is connected to a source of constant emf of

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. Then, the switch was shifted to contact 2 from contact 1 . Find the amount of heat generated in the

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resistance.

Topic:

Electrostatic Potential and Capacitance

Book:

Electricity and Magnetism (DC Pandey)

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Practice more questions from Electrostatic Potential and Capacitance

Question 1

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Calculate the area of the plates of a one farad parallel plate capacitor if separation between plates is

1 mm

and plates are in vacuum.

$18 \times 1 0^{8} m^{2}$
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$1.3 \times 1 0^{8} m^{2}$
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Question 2

Hard

A

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Question 3

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There are two thin wire rings, each of radius

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Question 4

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Find charges on different capacitors.

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Electrostatic Potential and Capacitance

Book:

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Practice questions on similar concepts asked by Filo students

Question 1

In the circuit shown in figure, the capacitor is partially charged with a charge

q_{0} = CV /2

and at

t = 0

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t

Topic:

Magnetism, EMI and AC

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Question 2

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Question 3

QUESTION 26 The atomic diameter of a BCC crystal structure (if a is the lattice parameter) is: A. a B. a/2 C. (4/âˆš3)a D. (âˆš3/4)a QUESTION 27 Aluminum has an FCC structure with an atomic radius of 0.143 nm and an atomic weight of 26.98 g/mol. Avogadroâ€™s number is 6.023 x 10^23 atoms/mol. The calculated density of Aluminum is: A. 0.678 g/cm^3 B. 1.35 g/cm^3 C. 2.71 g/cm^3 D. 6.11 g/cm^3 QUESTION 28 What is the planar density of atoms in the (110) plane in question 27 (above)? A. 2 atoms/nm^2 B. 6.11 atoms/nm^2 C. 8.64 atoms/nm^2 D. 12.27 atoms/nm^2 QUESTION 29 The density of niobium is 8.58 g/cm^3. Its atomic mass is 92.91 g/mol and its structure is BCC. Avogadroâ€™s number is 6.023 x 10^23 atoms/mol. Calculate the lattice parameter and radius of niobium: A. a = 3.3 cm ; R = 0.143 cm B. a = 0.33 nm ; R = 0.143 nm C. a = 0.33 nm ; R = 0.467 nm D. a = 3.3 cm ; R = 0.467 cm E. a = 3.3 nm ; R = 0.467 nm QUESTION 30 The lattice constant of a unit cell of a cube is 3.28 Angstrom. The interplanar spacing (210) plane is: A. 0.986 Angstrom B. 1.093 Angstrom C. 1.467 Angstrom D. 1.641 Angstrom QUESTION 31 The interplanar spacing between (122) planes found to be 2.35 Angstrom. The lattice constant in the case of a simple cubic is: A. 0.261 Angstrom B. 0.783 Angstrom C. 7.05 Angstrom D. 21.15 Angstrom

Topic:

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Question 4

Types of Preference Shares. Types of Preference Slares

Cumulative and Non-cumulative Preference Shares ⎦ ⎤ ⎣ ⎡ Participating and Nonparticipating Preference Shares ⎦ ⎤ Convertible and Non eonvertible Preference Shares ⎦ ⎤

Redeemable and Irrodeemable which dividend goes on accumulating until it is fully paid. is not paid in one or more years due to inadequate profits, then this unpaid dividend gets accumulated. This accumulated dividend is paid when company performs well The arrears of dividend are paid before making payment to equity shareholders. The preference shares are always cumulative unless oth of Association. It means that if dividend is not paid any year, the unpaid amount is carried forward to the next year and so on, until all arrears have been paid. Non-cumulative Preference Shares : Dividend on accumulated. This means, the dividend on shares can be paid only out of profits ef theses does not get in that particular year. If dividend is not paid in any year, it is lost forever. 3. Participating Preference Shares: The holders of these shares are entitled to participate in surplus profit besides preferential dividend. The surplus profit which remains after the dividend has been paid to equity shareholders, up to certain limit, is distributed to preference shareholders. 4. Non-participating Preference Shares: The preference shares are deemed to be non-participating, if there is no clear provision in the Articles of Association. These shareholders are entitled to fixed rate of divided, prescribed at the time of issue. 5. Convertible Preference Shares : The holders of these shares have a right to convert their preference shares into equity shares. The conversion takes place within a certair fixed period. 6. Non-convertible Preference Shares : These shares cannot be converted into equi shares, 7. Redeemable Preference Shares : Shares which can be redeemed after certain fir period of time are called redeemable preference shares. A company limited by sha if authorised by Articles of Association, issues redeemable preference shares. shares must be fully paid. These shares are redeemed out of divisible profit or out of fresh issue of shares made for this purpose. 8. Irredeemable Preference Shares : Shares which are not redeemable i.e. p only on winding up of the company are called irredeemable preference shar per Section 55(1) of the Companies Act 2013, a company cannot issue irrede preference shares.

Topic:

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Question Text	The equivalent capacitance of the arrangement shown in figure, if $A$ is the area of each plate, is
Topic	Electrostatic Potential and Capacitance
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	54

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