- The potential energy of an electric dipole in a uniform electric field is
U = − p ⋅ E = − pE cos θ - When the dipole is parallel to the field (θ = 0∘),
U = − pE
This is the minimum potential energy (stable equilibrium). - When the dipole is perpendicular to the field (θ = 90∘),
U = 0 - When the dipole is anti-parallel to the field (θ = 180∘),
U = +pE
This corresponds to an unstable equilibrium. - Work done in rotating the dipole through an angle θ\thetaθ is W = pE(1 − cosθ) and this work equals the increase in potential energy.
Definitions [34]
Definition: Electrostatic Potential Energy
Electrostatic potential energy is the energy stored in a system of charges due to their relative positions.
Core Idea: If an external force moves a test charge against the electrostatic force, the work done by the external agent is stored as electrostatic potential energy.
Definition: Electrostatic Potential
Electrostatic potential at a point is the work done by an external agent in bringing a unit positive test charge slowly from infinity to that point without acceleration.
Definition: Electrostatic Potential Difference
The potential difference between two points P and R is the work done by an external force in moving a unit positive test charge from one point to the other.
Definition: Electric Potential Due to a Point Charge
The work done by an external agent in bringing a unit positive test charge slowly from infinity to a point in an electric field, against the electrostatic force, is called the electric potential at that point.
Definition: Electric Dipole
An electric dipole is a pair of equal and opposite charges separated by a small distance.
Definition: Dipole Length
If the charges are separated by a distance 2a2a, then 2a2a is called the dipole length.
Definition: Electrostatic Potential
The electrostatic potential V at a point in an electric field is defined as the work done by an external force in bringing a unit positive charge (without acceleration) from infinity to that point.
Definition: Equipotential Surface
The surface at which electric potential is the same at each point is called an equipotential surface.
Definition: Electrostatic Shielding
The phenomenon in which the electric field inside a cavity of a conductor is zero, irrespective of external charges or fields, is called electrostatic shielding.
Definition: Capacity of Conductor
The ability of a conductor to store charge is called the capacity of conductor.
Definition: Capacitor
A system consisting of two conductors having equal and opposite charges separated by an insulator or dielectric is called a capacitor.
Definition: Dielectric Strength
The maximum electric field that a dielectric medium can withstand without breakdown (of its insulating property) is called its dielectric strength.
Definition: Capacitance
The ratio of the charge Q given to one of the conductors of a capacitor to the potential difference V between the conductors is called its capacitance, given by C = Q/V.
Definition: The Parallel Plate Capacitor
A capacitor that consists of two large, parallel, conducting plates separated by a small distance is called a parallel plate capacitor.
Definition: Dielectric Constant
The ratio of the permittivity of a medium to the permittivity of vacuum.
K = ε / ε₀
OR
Dielectric constant is the factor by which the capacitance of a capacitor increases when a dielectric is completely inserted between its plates.
Definition: Permittivity of a Medium
The product of vacuum permittivity and dielectric constant of the medium.
ε = ε₀K
Definition: Energy Stored in a Capacitor
The work done in the transfer of charge q between the two plates of a capacitor, which gets stored in the form of potential energy of the system, is called the energy stored in a capacitor.
Definition: Electric Potential Energy
The electric potential energy of a system of charges is the work that has been done in bringing those charges from infinity to near each other to form the system.
OR
The total work done by an external agency in assembling the charges from infinity to their specified positions (without acceleration), is called the electrostatic potential energy of the system.
Definition: Potential Gradient
The rate of change of potential with distance in the electric field is called the 'potential gradient'.
Definition: Electric Potential at a Point
The work done by an external agent in carrying a unit positive test charge from infinity to a point in the electric field is called the electric potential at that point.
OR
The work done in bringing a unit positive charge (without acceleration) from infinity to a given point in an electric field, is called electrostatic potential at that point.
Definition: Electric Dipole Moment
The product of the magnitude of one charge and the separation vector directed from negative to positive charge, is called the electric dipole moment.
\[\vec p\] = q × (2\[\vec a\])
Definition: Electric Dipole
An electric dipole is a pair of equal and opposite point charges, placed at a small distance. Its moment, known as electric dipole moment.
OR
A system of two equal and opposite charges separated by a small distance, is called an electric dipole.
Definition: Electron-volt
1 electron-volt is the work done in taking one electron from one point to the other, when the potential difference between these points is 1 volt.
OR
1 electron-volt is the (kinetic) energy which an electron acquires when accelerated through a potential difference of 1 volt.
Definition: Equipotential Surface
Any surface over which the electric potential is same everywhere is called an equipotential surface.
OR
A surface on which the electric potential has the same value at every point, is called an equipotential surface.
Definition: Electric Polarisation
To sum up, an electric field produces in a dielectric (non-polar or polar) a net dipole moment in the direction of the field. This phenomenon is known as 'dielectric polarisation' or 'electric polarisation of matter'.
Definition: Polar Dielectric Molecule
A ‘polar' molecule is one in which the centre of gravity of the positive charges (protons) is separated from the centre of gravity of the negative charges (electrons) by a finite distance.
OR
A molecule in which the centres of positive and negative charges are separated, giving it a permanent dipole moment, is called a polar molecule.
Definition: Energy Stored in a Charged Capacitor
“The total amount of work in charging the capacitor is stored up in the capacitor in the form of electric potential energy.”
Definition: Dielectric
The dielectric constant (or specific inductive capacity) of a material is the ratio of the capacitance of a given capacitor completely filled with that material to the capacitance of the same capacitor in vacuum.
OR
A non-conducting substance that has no (or negligible) free charge carriers and can be polarised in an external electric field, is called a dielectric.
Definition: Non-polar Dielectric Molecule
The Molecules in which the centres of positive and negative charges coincide and so the molecules have zero electric dipole moment. Such molecules are called ‘non-polar' molecules.
OR
A molecule in which the centres of positive and negative charges coincide and has no permanent dipole moment, is called a non-polar molecule.
Definition: Dielectric Strength
Dielectric strength is defined as the maximum value of the electric field that it can tolerate without its electric breakdown.
Definition: Capacitance of a Capacitor
The capacitance of a capacitor is defined as the ratio of the charge given to a plate of the capacitor to the potential difference produced between the plates.
Definition: Capacitance of a Conductor
The capacitance of a conductor is defined as the ratio of the charge given to the rise in the potential of the conductor.
Mathematical definition: C = \[\frac {Q}{V}\]
Definition: Parallel Plate Capacitor
A capacitor consisting of two large parallel conducting plates separated by a small distance is called a parallel plate capacitor.
Definition: Capacitor
A capacitor is a pair of two conductors of any shape which are close to each other and have equal and opposite charges. These conductors are called the 'plates' of the capacitor.
OR
A system of two conductors separated by an insulator, is called a capacitor.
Formulae [30]
Formula: Electrostatic Potential Difference
If the potential energies at points P and R are UP and UR, then
\[V_P-V_R=\frac{U_P-U_R}{q}\]
Formula: Electrostatic Potential
If the work done in bringing charge q from infinity to point P is W, then
VP = \[\frac {W}{q}\]
Formula: Electric Potential due to a Point Charge
V = \[\frac{1}{4\pi\varepsilon_0}\cdot\frac{q}{r}\]
Varies on spherical shell carrying charge q and radius R:
- Inside shell (r < R): V = \[\frac {1}{4πε_0}\] ⋅ \[\frac {q}{R}\]
- On surface (r = R): V = \[\frac {1}{4πε_0}\] ⋅ \[\frac {q}{R}\]
- Outside shell (r > R): V = \[\frac {1}{4πε_0}\] ⋅ \[\frac {q}{r}\]
Formula: Potential Due to a Point Charge
\[V=\frac{Q}{4\pi\varepsilon_0r}\]
Potential due to System of Charges:
\[U=\frac{1}{4\pi\varepsilon_0}\frac{q_1q_2}{r_{12}}\]
Formula: Electric Potential Energy of Two Point Charges
U = \[\frac{1}{4\pi\varepsilon_0}\cdot\frac{q_1q_2}{r_{12}}\]
Formula: In a medium of dielectric constant K K
\[V(r)=\frac{1}{4\pi\varepsilon_0K}\frac{q}{r}\]
- V(r) = electric potential at distance rr from the charge
- q = source charge
- ε0 = permittivity of free space
- K = dielectric constant of medium
- Reference is taken such that V(∞) = 0.
Formula: Potential Due to an Electric Dipole
\[V=\frac{1}{4\pi\varepsilon_{0}}\cdot\frac{p\cos\theta}{r^{2}}=\frac{1}{4\pi\varepsilon_{0}}\cdot\frac{\vec{p}\cdot\vec{r}}{r^{3}}(r>>a)\]
Formula: Electric Dipole Moment
The electric dipole moment is:
\[\vec{p}=q(2a)\hat{p}\]
Its direction is from the negative charge to the positive charge.
Formula: Electrostatic Potential
V = \[\frac{W_{\infty\to P}}{q_{0}}\] (Work done per unit positive charge)
SI Unit: Volt (V) = Joule/Coulomb (J/C);
Dimensional Formula: [M1L2T−3A−1]
Formula: Potential Energy of a System of Charges
\[V=\frac{1}{4\pi\varepsilon_{0}}\left[\frac{q_{1}}{r_{1}}+\frac{q_{2}}{r_{2}}+\frac{q_{2}}{r_{3}}+\frac{q_{4}}{r_{4}}+.........+\frac{q_{n}}{r_{n}}\right]\]
\[V=\frac{1}{4\pi\varepsilon_0}\sum_{i=1}^{i=n}\frac{q_i}{r_i}\]
Formula: Electric Field on a Charged Conductor Surface
\[\vec{E}=\frac{\sigma}{\varepsilon_0}\hat{n}\]
where
σ = surface charge density
\[\hat n\] = outward normal unit vector
Magnitude form:
E = \[\frac{\sigma}{\varepsilon_0}\]
Formula: Cylindrical Capacitor
C = \[\frac {2πkε₀ l}{2.303 log(b/a)}\]
Formula: Spherical Capacitor
C = 4πkε₀ · [\[\frac {ab}{(b − a)}\]]
Formula: Basic Capacitance
C = Q/V
Formula: Capacitance of a Parallel Plate Capacitor
For two plates separated by distance d:
\[C=\frac{\varepsilon_0A}{d}\]
With a dielectric medium:
\[C=\frac{K\varepsilon_0A}{d}\]
Formula: Energy Stored / Work Done in a Capacitor
W = \[\frac {1}{2}\]qV
Formula: Dipole Potential on Axial Line
V = \[\frac{1}{4\pi\varepsilon_0}\frac{P}{r^2-l^2}\]
Far-field, r ≫ 2l: V = \[\frac{1}{4\pi\varepsilon_{0}}\frac{p}{r^{2}}\] volt.
Formula: Potential Difference between Two Points
\[V_A-V_B=\frac{W}{q_0}\]
OR
\[V_P-V_R=\frac{U_P-U_R}{q}\]
Formula: Electron-volt
1 electron-volt = 1.6 × 10-1 joule.
Formula: Potential Due to a System of Charges
Potential due to a continuous charge distribution:
\[V=\frac{1}{4\pi\varepsilon_0}\int\frac{\rho dV}{r}\]
Potential outside a uniformly charged spherical shell:
\[V=\frac{1}{4\pi\varepsilon_0}\frac{q}{r}\quad(r\geq R)\]
Potential inside a uniformly charged spherical shell:
\[V=\frac{1}{4\pi\varepsilon_0}\frac{q}{R}\quad(r<R)\]
Formula: Work Done in Rotating an Electric Dipole
W = pE (cos θ1 – cos θ2)
Formula: Electric Potential Due to a Point Charge
V = \[\frac{1}{4\pi\varepsilon_0}\frac{q}{r}\] volt
Formula: Electric Potential
V = \[\frac {W}{q_0}\]
- Dimensions: [V] = [ML2T−3A−1]
- SI unit is volt (V), where 1 V =1 J C−1
OR
\[V=\frac{W_{\infty\to P}}{q}\]
Unit: 1 volt=1 joule per coulomb (J/C)
Formula: Potential at any Point
V = \[\frac{1}{4\pi\varepsilon_{0}}\frac{p\cos\theta}{r^{2}}\] volt.
Formula: Electric Potential Energy of Two Point Charges
U = \[\frac{1}{4\pi\varepsilon_{0}}\frac{q_{1}q_{2}}{r}joule\]
Formula: Relation between Electric Field and Potential
E = -\[\frac {dV}{dl}\]
Formula: Energy Stored in a Charged Capacitor
\[U=\frac{1}{2}\frac{Q^{2}}{C}=\frac{1}{2}CV^{2}joule.\]
Formula: Capacitance of a Parallel-Plate Capacitor
C = \[\frac{K\varepsilon_0A}{d}\] farad
If there is vacuum (or air) between the plates, then K = 1
C0 = \[\frac {ε_0 A}{d}\] farad
Formula: Capacitance of an Isolated Spherical Conductor
C = 4 π ε0 a farad
Formula: Potential Energy of a Charged Conductor
U = \[\frac {1}{2}\] C V2
Key Points
Key Points: Electric Potential Due to a Point Charge
- Electric potential at a point is the work done per unit positive test charge in bringing it slowly from infinity to that point, against the electric field.
- For a point charge q in air/vacuum:
V(r) = \[\frac{1}{4\pi\varepsilon_0}\frac{q}{r}\] - In a medium of dielectric constant K:
V(r) = \[\frac{1}{4\pi\varepsilon_0K}\frac{q}{r}\] - Positive charge produces positive potential; negative charge produces negative potential.
- Potential due to a point charge is spherically symmetric and depends only on distance r.
- Distance dependence:
F ∝ 1/r2, E ∝ 1/r2, V ∝ 1/r. - The potential at infinity is taken as zero; only potential differences are physically significant.
- The electrostatic field is conservative, so the work done in moving a charge between two points is path independent.
Key Points: Capacitors
- Capacitance depends on the geometry (shape, size, separation) of the conductors and on the dielectric between them.
- In a series, the charge on each capacitor is the same, but the voltage across each is different.
- A series combination divides high voltage — the capacitor with the smallest capacitance gets the largest P.D., and it cannot store much charge.
- In parallel, the voltage across each capacitor is the same, but the charge on each is different, and it handles only low voltage.
- A parallel combination is used when a large capacitance at low potential is needed, as it can store a large amount of charge.
Key Points: Combination of Capacitors
Capacitors in Series:
Equivalent capacitance: \[\frac{1}{C_s}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+\cdots\]
- Same voltage (V) across all capacitors
- Charge divides
- The equivalent capacitance is greater than the largest capacitor
Capacitors in Parallel:
\[C_p=C_1+C_2+C_3+\cdots\]
- Same voltage (V) across all capacitors
- Charge divides
- The equivalent capacitance is greater than the largest capacitor
Key Points: Electric Potential Energy of an Electric Dipole at Electrostatic Field
Key Points: Properties of Equipotential Surfaces
- Zero Work: No work is done in moving a charge along an equipotential surface because the potential difference is zero.
- Relation with Electric Field: The electric field is always perpendicular to an equipotential surface; there is no electric field component along the surface.
- Spacing and Field Strength: Equipotential surfaces are closer where the electric field is strong and farther apart where the field is weak.
- Non-intersection: Equipotential surfaces never intersect, since that would imply two directions of the electric field at one point, which is impossible.
Key Points: Dependence of the Capacitance of a Capacitor
- Capacitance is directly proportional to the area of the plates
C ∝ A
Increasing the effective overlapping area increases capacitance. - Capacitance is inversely proportional to the distance between the plates
C ∝ \[\frac {1}{d}\]Reducing the separation between plates increases capacitance. - Capacitance depends on the medium between the plates
It increases when a dielectric is introduced and is directly proportional to the dielectric constant K:
C ∝ K
Key Points: Electric Polarisation of Matter
- An electric field produces dipoles in non-polar dielectrics and aligns them in polar dielectrics, resulting in a net dipole moment along the field.
- Polarisation causes bound charges to appear only on the surfaces of the dielectric slab; the interior remains electrically neutral.
- The polarisation charges create an electric field opposite to the applied field, reducing the field inside the dielectric.
- When a dielectric is inserted in an isolated capacitor, the electric field and potential difference decrease, while capacitance increases.
- A dielectric can withstand the electric field only up to a certain limit, beyond which electrical breakdown occurs.
Key Points: Conductors and Insulators (or Dielectrics)
- In metals, electric current is due to the drift of free electrons; positive ions remain fixed in the lattice and do not move.
- Valence electrons in the outermost orbit are loosely bound and can become free (conduction) electrons, especially at room temperature.
- When an external electric field is applied to a conductor, free electrons acquire a drift velocity opposite to the field, producing current.
- The electrical conductivity of a solid depends on the number of free electrons available for conduction.
- In dielectrics, an applied electric field causes electric polarisation; charges appear on the surface, but no charge flows through the material.
Key Points: Combinations of Capacitors
- Series combination: All capacitors connected in series carry the same charge Q, while the total potential difference is the sum of individual potential differences.
- Equivalent capacitance in series is given byand is less than the smallest individual capacitance.
- In a series combination, the potential difference across each capacitor is inversely proportional to its capacitance, and the capacitor with the least capacitance has the highest voltage.
- Parallel combination: All capacitors connected in parallel have the same potential difference, while the charge distributes according to capacitance.
- Equivalent capacitance in parallel is given byand is greater than any individual capacitance.
Important Questions [83]
- An Electric Dipole is Held in a Uniform Electric Field.(I) Show that the Net Force Acting on It is Zero.
- A point P lies at a distance x from the midpoint of an electric dipole on its axis. The electric potential at point P is proportional to ______.
- Derive an Expression for the Electric Potential at Any Point Along the Axial Line of an Electric Dipole.
- Draw a Sketch of Equipotential Surfaces Due to a Single Charge (-q), Depicting the Electric Field Lines Due to the Charge
- Depict the Equipotential Surface Due to (I) an Electric Dipole, (Ii) Two Identical Positive Charges Separated by a Distance.
- Draw the Equipotential Surfaces Due to an Electric Dipole.
- Two identical point charges, q each, are kept 2m apart in the air. A third point charge Q of unknown magnitude and sign is placed on the line joining the charges such that the system remains in
- Depict the equipotential surfaces for a system of two identical positive point charges placed a distance(d) apart?
- Why is There No Work Done in Moving a Charge from One Point to Another on an Equipotential Surface?
- Draw the Equipotential Surfaces Due to an Electric Dipole. Locate the Points Where the Potential Due to the Dipole is Zero.
- Draw Equipotential Surfaces in the Case of a Single Point Charge and in a Constant Electric Field in Z-direction. Why the Equipotential Surfaces About a Single Charge Are Not Equidistant? and Can Electric Field Exist Tangential to an Equipotential Surface? Give Reason
- What is the Geometrical Shape of Equipotential Surfaces Due to a Single Isolated Charge?
- Write two important characteristics of equipotential surfaces.
- Define an Equipotential Surface.
- If an external electric field (E) is applied on the system, write the expression for the total energy of this system.
- Why is Electrostatic Potential Constant Throughout the Volume of the Conductor and Has the Same Value (As Inside) on Its Surface?
- Deduce the Expression for the Electrostatic Energy Stored in a Capacitor of Capacitance 'C' and Having Charge 'Q'.
- How Will the (I) Energy Stored and (Ii) the Electric Field Inside the Capacitor Be Affected When It is Completely Filled with a Dielectric Material of Dielectric Constant K?
- A Hollow Metal Sphere of Radius 10 Cm is Charged Such that the Potential on Its Surface is 5 V. What is the Potential at the Centre of the Sphere?
- Two-point charges q1 and q2 are kept at a distance of r12 in air. Deduce the expression for the electrostatic potential energy of this system.
- Justify your answers for each case. State the significance of the negative value of electrostatic potential energy of a system of charges.
- Four Point Charges Q, Q, Q and Q Are Placed at the Corners of a Square of Side 'A' as Shown in the Figure.
- Find Out the Amount of the Work Done to Separate the Charges at Infinite Distance.
- A Point Charge Q is Placed at Point 'O' as Shown in the Figure. is the Potential at Point A, I.E. Va, Greater, Smaller Or Equal to Potential, Vb, at Point B, When Q is (I) Positive, and (Ii) Negative
- 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.
- A Point Charge Q is Placed at Point O as Shown in the Figure. the Potential Difference Va – Vb Positive. is the Charge Q Negative Or Positive?
- Figure Shows the Field Lines Due to a Positive Point Charge. Give the Sign of Potential Energy Difference of a Small Negative Charge Between the Points Q and P.
- A Capacitor of 200 Pf is Charged by a 300 V Battery. the Battery is Then Disconnected and the Charge Capacitor is Connected to Another Uncharged Capacitor of 100 Pf.
- Deduce the Expression for the Potential Energy of a System of Two Charges
- Deduce the Expression for the Potential Energy of a System of Two Point Charges Q1 and Q2 Brought from Infinity to the Points → R 1 and → R 2 Respectively
- Depict the orientation of an electric dipole in (a) stable and (b) unstable equilibrium in an external uniform electric field. Write the potential energy of the dipole in each case.
- A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor? If another capacitor of 6 pF is connected in series with it with the same battery connected across the combination, find the charge stored and potential difference across each capacitor.
- Define electrostatic potential at a point. Write its S.I. unit. Three point charges q1, q2 and q3 are kept respectively at points A, B, and C as shown in the figure,
- A point charge is placed at the centre of a hollow conducting sphere of internal radius ‘r’ and outer radius ‘2r’. The ratio of the surface charge density of the inner surface to that of the outer
- 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
- A Capacitor of Unknown Capacitance is Connected Across a Battery of V Volts. the Charge Stored in It is 300 μC.
- 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?
- Define Capacitor Reactance. Write Its S.I Units.
- Find the Equivalent Capacitance of the Network
- 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
- The Figure Show a Network of Five Capacitors Connected to a 10v Battery. Calculate the Charge Acquired by the 5μF Capacitor.
- A capacitor of capacitance ‘C’ is charged to ‘V’ volts by a battery. After some time the battery is disconnected and the distance between the plates is doubled.
- A Capacitor of Capacitance ‘C’ is Charged to ‘V’ Volts by a Battery. After Some Time the Battery is Disconnected and the Distance Between the Plates is Doubled. Now a Slab of Dielectric Constant, 1 < K < 2, is Introduced to Fill the Space Between the Plates.
- Three Circuits, Each Consisting of a Switch 'S' and Two Capacitors, Are Initially Charged, as Shown in the Figure. After the Switch Has Been Closed, in Which Circuit Will the Charge on the Left-hand
- Read the following paragraph A capacitor is a system of two conductors separated by an insulator. Find the equivalent capacitance between points A and B in the given diagram.
- A Capacitor of Capacitance C is Charged Fully by Connecting It to a Battery of Emf E. It is Then Disconnected from the Battery.
- A Bulb is Connected in Series with a Variable Capacitor and an Ac Source as Shown. What Happens to the Brightness of the Bulb When the Key is Plugged in and Capacitance of the Capacitor is Gradually Reduced?
- The variation of inductive reactance (XL) of an inductor with the frequency (f) of the ac source of 100 V and variable frequency is shown in fig. (i) Calculate the self-inductance of the inductor.
- When an Ac Source is Connected to an Ideal Capacitor, Show that the Average Power Supplied by the Source Over a Complete Cycle is Zero
- A parallel plate capacitor (A) of capacitance C is charged by a battery to voltage V. The battery is disconnected and an uncharged capacitor (B) of capacitance 2C is connected across A. Find the ratio
- 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.
- Two Identical Parallel Plate Capacitors a and B Are Connected to a Battery of V Volts with the Switch S Closed.
- Find equivalent capacitance between A and B in the combination given below. Each capacitor is of 2 µF capacitance.
- 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 Reaso
- 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.
- 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.
- 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.
- 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.
- Answer the Following Question. Describe Briefly the Process of Transferring the Charge Between the Two Plates of a Parallel Plate Capacitor When Connected to a Battery.
- Define the Capacitance of a Capacitor. Obtain the Expression for the Capacitance of a Parallel Plate Capacitor in Vacuum in Terms of Plate Area a and Separation D Between the Plates.
- Solve the Following Question. a Parallel Plate Capacitor is Charged by a Battery to a Potential Difference V. It is Disconnected from the Battery and Then Connected to Another Uncharged Capacitor
- A Slab of Material of Dielectric Constant K Has the Same Area as the Plates of a Parallel Plate Capacitor but Has a Thickness
- 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.
- Explain Briefly the Process of Charging a Parallel Plate Capacitor When It is Connected Across a D.C. Battery
- 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.
- A 10 V Battery of Negligible Internal Resistance is Connected Across a 200 V Battery and a Resistance of 38ω as Shown in the Figure. Find the Value of the Current in Circuit.
- 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
- A 5 V Battery of Negligible Internal Resistance is Connected Across a 200 V Battery and a Resistance of 39ω as Shown in the Figure. Find the Value of the Current in Circuit.
- An ac circuit consists of a series combination of circuit elements X and Y. The current is ahead of the voltage in phase by pi/4
- An Ac Circuit Consists of a Series Combination of Circuit Elements X and Y. the Current is Ahead of the Voltage in Phase by π 4 . If Element X is a Pure Resistor of 100ω ,
- Find the Amount of Work Done in Moving a Charge Q Over a Closed Loop a B C D A.
- The figure shows a network of five capacitors connected to a 100 V supply. Calculate the total energy stored in the network.
- A Circuit is Set up by Connecting Inductance L = 100 Mh, Resistor R = 100 ω and a Capacitor of Reactance 200 ω in Series. an Alternating Emf of 150 √ 2 V, 500/π Hz is Applies Across this Series
- A Capacitor 'C', a Variable Resistor 'R' and a Bulb 'B' Are Connected in Series to the Ac Mains in Circuit
- Two Capacitors of Unknown Capacitances C1 and C2 Are Connected First in Series and Then in Parallel Across a Battery of 100 V.
- 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 ______.
- Obtain the expression for the energy stored in a capacitor connected across a dc battery.
- A parallel plate capacitor (A) of capacitance C is charged by a battery to voltage V. The battery is disconnected and an uncharged capacitor (B) of capacitance 2C is connected across A.
- In the Following Arrangement of Capacitors, the Energy Stored in the 6 µF Capacitor is E. Find the Value of the Following : (I) Energy Stored in 12 µF Capacitor. (Ii) Energy Stored in 3 µF Capacitor.
- Find the Charge on the Capacitor as Shown in the Circuit.
- Find the Ratio of Energy Stored in the Two Configurations If They Are Both Connected to the Same Source.
- Obtain the Expression for the Energy Stored per Unit Volume in a Charged Parallel Plate Capacitor.
Concepts [20]
- Electric Potential and Potential Energy
- Electrostatic Potential
- Electric Potential Due to a Point Charge
- Potential Due to an Electric Dipole
- Potential due to a System of Charges
- Equipotential Surfaces
- Relation Between Electric Field and Electrostatic Potential
- Potential Energy of a System of Charges
- Potential Energy of a Single Charge
- Potential Energy of a System of Two Charges in an External Field
- Potential Energy of a Dipole in an External Field
- Electrostatics of Conductors
- Dielectrics and Polarisation
- Capacitors and Capacitance
- The Parallel Plate Capacitor
- Effect of Dielectric on Capacitance
- Combination of Capacitors
- Energy Stored in a Charged Capacitor
- Overview: Electric Potential
- Overview: Capacitors and Dielectrics
