Some Important Questions for CBSE Class 12 Physics

Chapter 1 - Electric Charges and Fields

Coulomb’s Law

Coulomb’s law states that Force exerted between two point charges:

• Is inversely proportional to the square of the distance between these charges and
• Is directly proportional to the product of the magnitude of the two charges
• Acts along the line joining the two point charges.

Here ε₀ = 8.854 x 10^-12 C² N^-1 m^-2is called permittivity of free space.

Forces between multiple charges – Superposition principle

As per the principle of superposition, the force on any charge due to a number of other charges is the vector sum of all the forces on that charge due to other charges, taken one at a time.

Electric Dipole

An electric dipole is a pair of equal and opposite point charges q and –q, separated by a distance of 2a.

• Direction from –q to q is the direction of the dipole.
• The mid-point of locations of –q and q is called the centre of the dipole.
• The total charge of an electric dipole is zero but since the charges are separated by some distance the electric field does not cancel out.
• The dipole moment is the mathematical product of the separation of the ends of a dipole and the magnitude of the charges (2a x q).
• Some molecules like H₂O, have permanent dipole moment as their charges do not coincide. These molecules are called polar molecules.
• Permanent dipoles have a dipole moment irrespective of any external Electric field.

Gauss’s Law

According to Gauss’s law, the total of the electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. The total electric flux through a closed surface is zero if no charge is enclosed by the surface.

• Gauss’s law is true for any closed surface, no matter what its shape or size.
• The term q on the right side of Gauss’s law includes the sum of all charges enclosed by the surface. The charges may be located anywhere inside the surface.
• In the situation when the surface is so chosen that there are some changes inside and some outside, the electric field [whose flux appears on the left side of Eq. (1.31)] is due to all the charges, both inside and outside S. The term q on the right side of Gauss’s law, however, represents only the total charge inside S.
• The surface that we choose for the application of Gauss’s law is called the Gaussian surface. The Gaussian surface can pass through a continuous charge distribution.
• Gauss’s law is useful for the calculation of the electrostatic field for the asymmetric system.
• Gauss’s law is based on the inverse square dependence on distance contained in the Coulomb’s law. Any violation of Gauss’s law will indicate a departure from the inverse square law.

Applications of Gauss’s Law

Field due to infinitely long straight uniformly charged wire

Field due to a uniformly charged infinitely plane sheet

Field due to a uniformly charged thin spherical shell

Electric Field Lines

Electric field lines are a pictorial way of representing electric field around a configuration of charges.

• An electric field line is a curve drawn in such a way that the tangent to it at each point is in direction of the net field at that point.
• The electric field is inversely proportional to the square of the distance; hence electric field near the charge is high and keeps on decreasing as we go farther from the charge. The electric field lines, however, remain constant but are very far apart (at higher distances) as compared to a lesser distance.

Chapter 2 - Electrostatic Potential and Capacitance.

Equipotential Surfaces

An equipotential surface is one where the potential is the same at every point on the surface. For a single charge,

• Since r is constant, the equipotential surfaces are concentric spherical surfaces centred at the charge.
• Electric field lines are radial starting from or ending at the charge for positive and negative charges respectively.

For any charge configuration, equipotential surface through a point is normal to the electric field at that point.

Electrostatic Potential due to an Electric Dipole

An electric dipole is an arrangement of two equal and opposite charges separated by a distance 2a. The dipole moment is represented by p which is a vector quantity.

• The potential due to a dipole depends on r (distance between the point where potential is calculated and the mid-point of the dipole) and the angle between position vector r and dipole moment p.
• Dipole potential is inversely proportional to square of r.

Chapter 3 - Current Electricity

VAN DE GRAAFF Generator

Van de Graaff generator is used to generate high voltages of the order of a few million volts. This results in the generation of large electric fields for experimental purposes.

Principle

• The inner sphere has a higher potential than the outer if the charge q is positive.
• If the two spheres are connected through a wire, the charge will flow from high to low potential.
• Thus, providing smaller potentials at the inner sphere will keep building large amount of charge at the outer sphere, till the breakdown field of air (3 x 10⁶ V/m) is reached.
• This accumulates close to millions of volts.

Construction

• A large spherical conducting shell (of few metre radius) is supported at a height several meters above the ground on an insulating column.
• A long narrow endless belt insulating material, like rubber or silk, is wound around two pulleys – one at ground level, one at the centre of the shell.
• This belt is kept continuously moving by a motor driving the lower pulley.
• It continuously carries a positive charge, sprayed on to it by a brush at ground level, to the top.
• There it transfers its positive charge to another conducting brush connected to the large shell.
• Thus positive charge is transferred to the shell, where it spreads out uniformly on the outer surface and a voltage difference of as much as 6 or 8 million volts (with respect to ground) can be built up.

Energy stored in a Capacitor

Energy is stored in the capacitor when work is done to move a positive charge from the negative conductor towards the positive conductor against the repulsive force.

Effect of dielectric on Capacitance

When a dielectric is present between the plates of a parallel plate capacitor fully occupying the region, the dielectric is polarized by the electric field. The surface charge densities are considered as σ_p and -σ_p.

The dielectric constant of a substance is the factor by which the capacitance increases from its vacuum value when the dielectric is fully inserted in between the plates of the capacitor.

Wheatstone bridge

• Wheatstone bridge is a special arrangement of resistors as shown in the figure.
• There are 4 resistances R₁, R₂, R_3, and R₄ arranged in such a manner that there is a galvanometer placed between the points B and D.
• The arm BD is known as galvanometer arm. AC is known as battery arm.
• And the circuit is connected to the battery across the pair of diagonally opposite points A and C.
• According to the Wheatstone bridge principle:-
  • If (R₁/R₂)=(R₃/R₄), then Bridge is said to be balanced.
  • If the bridge is balanced there is no current flowing through the galvanometer arm.

Mathematically:-

• Assume current across the galvanometer arm I_g =0;
• To prove:-(R₁/R₂) = (R₃/R₄)
• Applying loop law to the loop ABDA,
• There is no Emf, therefore,
• 0= I₁R₁ - (I-I₁)R₃ + IgR_G equation (i) where R_G = resistance of the galvanometer.
• Applying loop Law to the loop BCDB,
• No Emf, 0 = (I₁-Ig)R₂ – (I-I₁+I_g)R₄ + I_gR_G equation(ii)
• Putting I_g = 0 in equation(i) and (ii)
• I₁R₁ - (I-I₁) R₃ = 0 => I₁R₁ = (I-I₁) R₃   equation (iii)
• I₁R₂ – (I-I₁)R₄ = 0 => I₁R₂ = (I-I₁) equation(iv)
• Dividing equation(iii) with (iv)
• (R₁/R₂) =(R₃/R₄) Hence proved.

Kirchhoff’s First law: Junction law

• Junction Law is also known as Kirchhoff’s First Law.
• It states that at the junction, the sum of currents entering the junction is equal to the sum of currents leaving the junction.
• The junction is any point in the circuit.
• Consider a case where I₁ and I₂are the current entering the junction and,currentI₄ and I₅ are exiting out of the junction.
• According to Kirchhoff’s law; I₁+ I₂ =I₃+ I₄+ I_5.

Kirchhoff’s Second law: Loop law

• Loop law is also known as Kirchhoff’s Second Law.
• It states that in a closed-loop, algebraic sum of Emfsis equal to the algebraic sum of the product of resistances and respective currents flowing through them.
• Consider a simple circuit havingEmfs = E₁ and E₂; R₁ and R₂ =resistances; current =I₁ and I₂.
• Then according to this law: E₁+E₂=I₁R₁+ I₂R₂
• For example:-
  • Consider given figure, let EMFs be E₁ and E₂ internal resistances be R₁, R₂ and R₃.
  • Steps to use Kirchhoff’s law:-
    • Choose the loop to apply Kirchhoff’s law.
    • Assume any direction.
    • Emf is +ive if assumed direction leaving +ive terminal of the battery.
    • IR is +ive if the current in the assumed direction.
  • Consider closed loop ABCDFA, using the assumptions;
  • E₂=+R₂I₃ +R₃I₂ ;where I₃=current flowing through R₃
  • Closed loop FCDEF, +E₁= +I₁R₁ + I₃R₂
  • Closed loop ABDEA, -E₁ + E₂ = -I₁R₁ +I₂R₃
  • If the direction of current is taken opposite then
  • Closed loop ABCDFA ;- -E₂=-R₂I₃-R₃I₂
  • FCDEF; -E₁= -I₁R₁ - I₃R₂
  • ABDEA; +E₁ - E₂ = +I₁R₁ - I₂R₃

Combination of Resistors

Resistors can be combined in 2 ways:-

Resistors in Series: A series circuit is a circuit in which resistors are arranged in a single chain, resulting in common current flowing through them.

Circuit Diagram

• ‘N’ number of resistors can be joined together.
• As all the resistors are connected to each other as a result same amount of current flows through each resistor.
• But the Potential difference will be different in each resistor.
• Consider current flowing through all the resistors =I, Resistance across the first resistor = R₁.
• The potential difference across resistor R₁is V_1, V₁=IR₁(By ohm’s Law)
• Similarly V₂=IR₂, V₃= IR₃ and so on.
• Therefore Total Voltage V=V₁+V₂+V₃+….. +V_n
• IR_equivalent =IR₁+IR₂+IR₃+…. +IR_n where R_equivalent is the equivalent resistance of the circuit.
• =>R_equivalent = (R₁+ R₂+ R₃+….+R_n)
• Therefore if the resistances are connected in series then the total equivalent resistance of the circuit is equal to the sum of all the resistors in the circuit.

Resistors in Parallel:- A parallel circuit is a circuit in which the resistors are arranged with their heads connected together, and their tails connected together.

• The potential difference(V)across each resistor is the same.
• The amount of current flowing is different. This means I= I₁+I₂+I₃+…+I_n
• =>From Ohm’s law - (V/R_equivalent) = (V/R₁)+(V/R₂)+(V/R₃)+…..+(V/R_n)
• =>1/ R_equivalent =(1/ R₁+1/ R₂+1/R₃+….+1/R_n)
• Therefore if the resistances are connected in parallel then the total equivalent resistance of the circuit is equal to the sum of the reciprocal of all the resistors connected in the circuit.

Circuit diagram

Cells in Series

• Consider there are multiple cells and they are arranged in such a way that the positive terminal of one cell is connected to the negative terminal of the other cell and so on.
• This arrangement is knownas series combination.

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