Chapter 3: Current Electricity Short Questions | physics Class 12 CBSE

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Chapter 3: Current Electricity Short Questions | physics Class 12 CBSE | ByteNotes.in

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Question 1

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Define electric current and state its SI unit.

Electric current is the net charge flowing per unit time through a cross-section of a conductor: I = q/t for steady current.
For time-varying currents, it is defined as I(t) = lim(ΔQ/Δt) as Δt → 0, representing the instantaneous rate of charge flow.
The SI unit of current is the ampere (A), which is a base SI unit defined through the magnetic effects of current.

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Question 2

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Why is there no net electric current through a metallic conductor in the absence of an electric field?

In the absence of an electric field, conduction electrons undergo random thermal motion, colliding with fixed ions and emerging with random velocity directions.
Since the velocities are completely random, the number of electrons moving in any one direction equals the number moving in the opposite direction.
As a result, the average velocity of all electrons is zero, so there is no preferential direction of charge flow and hence no net current.

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Question 3

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State Ohm's law and write its mathematical form.

Ohm's law states that the electric current I through a conductor is proportional to the potential difference V across its ends, provided temperature and physical conditions remain constant.
Mathematically, V ∝ I, or V = RI, where R is the resistance of the conductor measured in ohms (Ω).
Equivalently, Ohm's law may be stated in microscopic vector form as j = σE, where σ is the conductivity of the material.

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Question 4

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What is resistivity? On what factors does it depend?

Resistivity ρ is an intrinsic property of a material that relates resistance to the geometry of a conductor through R = ρl/A.
Resistivity depends on the nature and composition of the material (e.g., metals vs. semiconductors have vastly different values).
It also depends on temperature: for metals, resistivity increases with temperature, while for semiconductors, it decreases with increasing temperature.

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Question 5

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Define drift velocity of electrons and write its expression in terms of electric field.

Drift velocity vd is the small average velocity acquired by free electrons in a conductor in the direction opposite to the applied electric field, due to the net force on them.
The expression for drift velocity is vd = eEτ/m, where e is the electron charge, E is the electric field, τ is the relaxation time, and m is the electron mass.
Although electrons are accelerated by the field, collisions with ions continuously randomise their motion, so they acquire only this small average drift velocity rather than continuously increasing speed.

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Question 6

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How does doubling the length of a conductor affect its resistance? Justify using the formula.

Doubling the length of a conductor doubles its resistance, since resistance is directly proportional to length: R ∝ l.
This can be understood by considering two identical slabs placed end-to-end: the same current flows through both, but the total potential difference is 2V, so by Ohm's law the combined resistance is R_C = 2V/I = 2R.
Mathematically, from R = ρl/A, if l is replaced by 2l while ρ and A remain constant, R becomes 2ρl/A = 2R.

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Question 7

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Define relaxation time and explain its role in determining resistivity.

Relaxation time τ is the average time interval between two successive collisions of a conduction electron with the fixed ions in a metallic conductor.
It appears in the drift velocity formula vd = eEτ/m and hence in the expression for resistivity ρ = m/(ne²τ).
A smaller relaxation time means more frequent collisions, lower drift velocity, and hence higher resistivity; thus τ directly governs how easily current flows in a conductor.

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Question 8

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Define mobility of charge carriers and write its SI unit.

Mobility μ is defined as the magnitude of the drift velocity acquired by a charge carrier per unit electric field: μ = |vd|/E.
From the drift model, μ = eτ/m for electrons, showing it depends on the relaxation time and the carrier's charge-to-mass ratio.
The SI unit of mobility is m²/Vs; it is always positive regardless of the sign of the charge carrier.

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Question 9

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Why does the resistivity of metals increase with temperature while that of semiconductors decreases?

Resistivity is given by ρ = m/(ne²τ). In metals, the number density n of free electrons does not change significantly with temperature.
As temperature increases, electrons move faster and collide more frequently with ions, reducing the relaxation time τ. Since ρ is inversely proportional to τ, resistivity increases for metals.
In semiconductors, increasing temperature generates many more free charge carriers (n increases significantly), which more than compensates the decrease in τ, resulting in a net decrease in resistivity.

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Question 10

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State three deviations (limitations) of Ohm's law observed in certain materials.

V ceases to be proportional to I: the V-I characteristic is non-linear, as seen in conductors where resistivity increases with current at constant temperature.
The V-I relationship depends on the sign of V: reversing the polarity does not produce a current of equal magnitude in the opposite direction, as in a diode.
The relationship between V and I is not unique: the same current can correspond to more than one value of V, as exhibited by GaAs (gallium arsenide).

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Question 11

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What is the temperature coefficient of resistivity? Write its expression and state its sign for metals.

The temperature coefficient of resistivity α is the fractional increase in resistivity per unit increase in temperature, defined from ρT = ρ₀[1 + α(T – T₀)].
It has dimensions of (Temperature)⁻¹ and is typically expressed in °C⁻¹ or K⁻¹.
For metals, α is positive, meaning resistivity increases with temperature; for semiconductors, α is effectively negative as their resistivity decreases with rising temperature.

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Question 12

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What is electromotive force (EMF) of a cell? How does it differ from terminal voltage?

EMF (ε) of a cell is the potential difference between the positive and negative terminals when no current is flowing (open circuit); it equals the work done per unit charge by the cell in moving charge through it.
Terminal voltage V is the actual potential difference across the cell terminals when current I is flowing, given by V = ε – Ir, where r is the internal resistance.
Thus terminal voltage is always less than EMF when current flows (during discharge), and it equals EMF only in the open circuit condition.

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Question 13

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Derive the expression for current in a circuit containing a cell of EMF ε and internal resistance r connected to an external resistance R.

The terminal voltage of the cell when current I flows is V = ε – Ir, where the term Ir represents the voltage drop across the internal resistance.
Since this terminal voltage V also appears across the external resistance R, by Ohm's law V = IR, giving IR = ε – Ir.
Solving for I: I = ε/(R + r). The maximum current (when R = 0) is Imax = ε/r.

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Chapter 3: Current Electricity | Short Questions

Define electric current and state its SI unit.

Why is there no net electric current through a metallic conductor in the absence of an electric field?

State Ohm's law and write its mathematical form.

What is resistivity? On what factors does it depend?

Define drift velocity of electrons and write its expression in terms of electric field.

How does doubling the length of a conductor affect its resistance? Justify using the formula.

Define relaxation time and explain its role in determining resistivity.

Define mobility of charge carriers and write its SI unit.

Why does the resistivity of metals increase with temperature while that of semiconductors decreases?

State three deviations (limitations) of Ohm's law observed in certain materials.

What is the temperature coefficient of resistivity? Write its expression and state its sign for metals.

What is electromotive force (EMF) of a cell? How does it differ from terminal voltage?

Derive the expression for current in a circuit containing a cell of EMF ε and internal resistance r connected to an external resistance R.

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