CBSE Class 12 Physics Syllabus

What is the relationship between electric field and potential?

The electric field is the negative gradient of potential: E = -dV/dr. The field points in the direction of decreasing potential.

Define potential difference between two points.

The potential difference between two points is the work done per unit positive charge in moving it from one point to the other: V_AB = W_AB/q.

What is an equipotential surface?

A surface on which the electric potential is the same at every point, so no work is done in moving a charge along it.

Why is the electric field always perpendicular to an equipotential surface?

If the field had a component along the surface, work would be done in moving a charge along it, contradicting the definition of an equipotential surface (constant potential). Hence E must be perpendicular.

What is the shape of equipotential surfaces for (a) a point charge and (b) a uniform field?

(a) Concentric spheres centred on the point charge. (b) Equally spaced parallel planes perpendicular to the field direction.

Define electric potential energy of a system of two point charges.

It is the work done in assembling the charges by bringing them from infinity to their positions: U = (1/4πε₀)(q₁q₂/r) for two charges separated by distance r.

What is the potential energy of a charge q placed at a point where the potential is V?

U = qV. This is the work done in bringing charge q from infinity to that point.

Define a capacitor and capacitance, and give the SI unit.

A capacitor is a device that stores electric charge and energy. Capacitance is the ratio of charge stored to the potential difference across it: C = Q/V. SI unit: farad (F) = coulomb/volt.

What is the capacitance of a parallel plate capacitor (vacuum between plates)?

C = ε₀A/d, where A is the plate area and d is the separation between plates.

How does inserting a dielectric of constant K affect a parallel plate capacitor's capacitance?

The capacitance increases by a factor K: C = Kε₀A/d. The dielectric reduces the effective field, increasing charge storage at a given voltage.

Give the formula for the equivalent capacitance of capacitors in series.

1/C_eq = 1/C₁ + 1/C₂ + 1/C₃ + ... The equivalent capacitance is less than the smallest individual capacitance, and each capacitor carries the same charge.

Give the formula for the equivalent capacitance of capacitors in parallel.

C_eq = C₁ + C₂ + C₃ + ... The equivalent capacitance is greater than the largest individual capacitance, and each capacitor has the same potential difference.

Give three equivalent expressions for the energy stored in a capacitor.

U = ½CV² = ½QV = Q²/(2C), where C is capacitance, Q is charge, and V is the potential difference.

What is the energy density (energy per unit volume) of the electric field in a capacitor?

u = ½ε₀E², where E is the electric field strength between the plates.

Define electric current and give its SI unit.

Electric current is the rate of flow of electric charge through a cross-section: I = Q/t (or dQ/dt). SI unit: ampere (A) = coulomb/second.

In what direction is conventional current taken, and how does it relate to electron flow in a conductor?

Conventional current is taken in the direction of flow of positive charge, which is opposite to the direction of actual electron flow in a metallic conductor.

State Ohm's law and give its formula.

At constant temperature, the current through a conductor is directly proportional to the potential difference across it: V = IR, where R is the resistance.

Define resistance and give its SI unit. Name a device that obeys and one that disobeys Ohm's law.

Resistance is the opposition to current flow: R = V/I. SI unit: ohm (Ω). A metal wire obeys Ohm's law (ohmic); a diode or semiconductor disobeys it (non-ohmic).

What is drift velocity of electrons?

The average velocity acquired by free electrons in a conductor under an applied electric field, superimposed on their random thermal motion. v_d = -eEτ/m, where τ is the relaxation time.

Give the relation between current and drift velocity.

I = neAv_d, where n is the number density of free electrons, e the electronic charge, A the cross-sectional area, and v_d the drift velocity.

What is relaxation time (τ) in the context of resistivity?

The average time interval between two successive collisions of an electron with the lattice ions in a conductor. Collisions are the origin of resistance.

What is the microscopic origin of resistivity in a conductor?

Resistivity arises from collisions of drifting electrons with the vibrating lattice ions; these collisions impede electron motion. ρ = m/(ne²τ), where smaller τ gives higher resistivity.

Define resistivity (specific resistance) and give its formula and SI unit.

Resistivity is a material property independent of dimensions: ρ = RA/L, so R = ρL/A. SI unit: ohm-metre (Ω·m).

Define electrical conductivity and state its relation to resistivity.

Conductivity (σ) is the reciprocal of resistivity: σ = 1/ρ. SI unit: siemens per metre (S/m) or (Ω·m)^-1.

Define mobility of charge carriers and give its formula and SI unit.

Mobility is the magnitude of drift velocity per unit electric field: μ = v_d/E = eτ/m. SI unit: m²/(V·s).

State the relation between conductivity, carrier density, and mobility.

σ = neμ, where n is the carrier number density, e the charge, and μ the mobility. Hence ρ = 1/(neμ).

Compare the resistivity of conductors, insulators, and semiconductors.

Conductors have very low resistivity (~10^-8 Ω·m), insulators have very high resistivity (~10^8 to 10^16 Ω·m), and semiconductors have intermediate resistivity (~10^-5 to 10^6 Ω·m).

How does resistance/resistivity of a metallic conductor vary with temperature?

For metals, resistance and resistivity increase with temperature because increased lattice vibrations cause more frequent collisions, reducing relaxation time.

Give the formula for the temperature dependence of resistance.

R_T = R₀[1 + α(T - T₀)], where α is the temperature coefficient of resistance (per °C). It is positive for metals.

How does the resistivity of a semiconductor vary with temperature, and why?

Resistivity of a semiconductor decreases with rising temperature (negative temperature coefficient) because more charge carriers are thermally generated, increasing conductivity despite increased lattice vibrations.