CUET UG Physics Booster Test - 3 Electron Dynamics and Drift -

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CUET UG Physics Booster Test - 3 Electron Dynamics and Drift

⏱️ 30 Minutes

❓ 20 Questions

📌 Answers are locked once submitted — results and explanations appear at the end.

CUET UG Physics Booster Test - 3 Electron Dynamics and Drift

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QUESTION 1 OF 20

Which of the following statements is correct regarding the collision dynamics between conduction electrons and fixed ions?
Statements:
1. The post-collision velocity direction is completely random and independent of the incoming direction.
2. The kinetic energy of the electron changes drastically during each thermal collision with an ion.
3. The collisions only randomize the velocity vectors without drastically altering the average speed.
4. An electron emerging from a collision retains its pre-collision speed exactly.

Answer Review

1 Which of the following statements is correct regarding the collision dynamics between conduction electrons and fixed ions?
Statements:
1. The post-collision velocity direction is completely random and independent of the incoming direction.
2. The kinetic energy of the electron changes drastically during each thermal collision with an ion.
3. The collisions only randomize the velocity vectors without drastically altering the average speed.
4. An electron emerging from a collision retains its pre-collision speed exactly.

A 1, 2 and 4 are correct

B 1, 3 and 4 are correct

C 2, 3 and 4 are correct

D 1, 2 and 3 are correct

💡 Short Explanation

�� Electron directions become randomized after collisions. �� Average thermal speed remains approximately unchanged. �� Collisions do not drastically alter electron kinetic energy.

✅ Correct Answer Explanation

In a metallic conductor, free electrons continuously collide with the fixed positive ions of the lattice. These collisions randomize the direction of electron motion, making the post-collision direction independent of the incoming direction. However, the collisions are primarily elastic in nature, so the speed and kinetic energy of the electrons do not change drastically. As a result, while the velocity vectors are continuously randomized, the average thermal speed remains nearly constant. Therefore, statements 1, 3, and 4 are correct. Statement 2 is incorrect because thermal collisions do not generally produce large changes in the kinetic energy of electrons.

❓ Why Other Options Are Incorrect

�� Option A → Statement 2 is incorrect.
�� Option C → Statement 2 is incorrect.
�� Option D → Statement 2 is incorrect.

🎯 Strategy

Used – Concept Application

Application
Apply the microscopic collision model of free electrons in metals.
Final Logic
Collisions randomize direction but do not drastically change electron speed.

🧠 Memory Trick

Random Direction → No Preferred Motion

📚 Class: XII | Book: NCERT Physics Part II | Chapter: Current Electricity | Topic: Electron Motion | Subtopic: Fixed Ion Collisions

2 The macroscopic consequence of completely random post-collision velocity directions is

A A localized, temperature-dependent net current emerging in any isolated conductor

B The inability of individual electrons to accelerate under a weak external field

C The strict mathematical zeroing of the average velocity of electrons when no external field is applied

D The spontaneous synchronization of electron movements yielding effectively infinite mobility

💡 Short Explanation

�� Random directions cancel each other. �� No preferred direction exists. �� Average velocity becomes zero.

✅ Correct Answer Explanation

In the absence of an external electric field, free electrons move randomly because of thermal energy. Since the post-collision directions are completely random, equal numbers of electrons move in opposite directions. Consequently, the vector sum of all electron velocities becomes zero: 1/N∑v_i=0 This implies that the average velocity of electrons is zero. Although individual electrons move at high thermal speeds, there is no net motion in any particular direction. Therefore, no macroscopic current exists in an isolated conductor. Hence, Option C is correct.

❓ Why Other Options Are Incorrect

�� Option A → Random motion does not create a net current.
�� Option B → Electrons can accelerate when an electric field is applied.
�� Option D → Random collisions do not synchronize electron motion.

🎯 Strategy

Used – Concept Application

Application
Use the concept of thermal equilibrium and random motion.
Final Logic
Random velocities cancel statistically, giving zero average velocity.

🧠 Memory Trick

Zero Average → No Current

📚 Class: XII | Book: NCERT Physics Part II | Chapter: Current Electricity | Topic: Average Motion | Subtopic: Random Post-Collision Velocity

3 If the individual thermal velocities v_i are completely random in three dimensions, evaluating the sum
1/N∑v_i
for an extremely large number of electrons N will be

A 0

B v_d

C ∣v_(average)∣

D √(3k_BT/m)

💡 Short Explanation

�� Thermal velocities are random. �� Opposite velocity components cancel. �� Average velocity becomes zero.

✅ Correct Answer Explanation

In thermal equilibrium, free electrons move randomly in all directions. For every electron moving in one direction, there is statistically another moving in the opposite direction. Therefore, when the vector velocities of a very large number of electrons are averaged, 1/N∑v_i=0 This does not mean electrons are stationary. Rather, their motions are equally distributed in all directions, producing complete cancellation of the vector average. Hence the correct answer is Option A.

❓ Why Other Options Are Incorrect

�� Option B → Drift velocity exists only when an electric field is applied.
�� Option C → Average speed is not the same as average velocity.
�� Option D → Represents thermal speed, not average velocity.

🎯 Strategy

Used – Statistical Reasoning

Application
Use symmetry of random motion in thermal equilibrium.
Final Logic
Equal probability in opposite directions leads to zero average velocity.

🧠 Memory Trick

Average Velocity = Zero

📚 Class: XII | Book: NCERT Physics Part II | Chapter: Current Electricity | Topic: Average Motion | Subtopic: Sum of Velocities

4 Incorrect statement regarding electron velocities in the strict absence of an electric field

A The number of electrons crossing any internal cross-section from left to right equals those from right to left.

B The electrons themselves are completely stationary in the atomic lattice.

C Individual free electrons move freely in straight lines between successive ion collisions.

D The average of all velocities immediately after any collision is strictly zero.

💡 Short Explanation

�� Free electrons are always moving. �� Motion is random in the absence of a field. �� Only the average velocity is zero.

✅ Correct Answer Explanation

Even when no electric field is present, free electrons possess thermal energy and continuously move through the conductor. Between collisions, they travel approximately in straight lines and undergo frequent collisions with lattice ions. Although individual electrons are always moving, their directions are random. Therefore, the average velocity is zero, and equal numbers cross any section in opposite directions. Statement B is incorrect because electrons are not stationary; they are in continuous thermal motion.

❓ Why Other Options Are Incorrect

�� Option A → Correct consequence of random motion.
�� Option C → Correct description of motion between collisions.
�� Option D → Correct statistical result.

🎯 Strategy

Used – Concept Application

Application
Apply the free-electron model of metallic conduction.
Final Logic
Electrons are always moving thermally, even when no current flows.

🧠 Memory Trick

No Field = Random Motion

📚 Class: XII | Book: NCERT Physics Part II | Chapter: Current Electricity | Topic: Average Motion | Subtopic: Zero Net Velocity

5 Match List I with List II

List I	List II
1. Negative sign in a=-eE/m	a. Electrostatic force magnitude
2. Mass m	b. Rate of change of velocity
3. Quantity eE	c. Indicates acceleration is antiparallel to electric field
4. Variable a	d. Determines inertial resistance

A 1-d, 2-c, 3-b, 4-a

B 1-a, 2-b, 3-d, 4-c

C 1-c, 2-a, 3-d, 4-b

D 1-c, 2-d, 3-a, 4-b

💡 Short Explanation

�� Electric force acts opposite to the field on electrons. �� Mass opposes acceleration. �� Acceleration is the rate of velocity change.

✅ Correct Answer Explanation

For an electron in an electric field, a=-eE/m The negative sign indicates that acceleration is opposite to the electric field because electrons carry negative charge. The quantity eE represents the magnitude of the electrostatic force acting on the electron. The mass m determines the inertia of the electron and its resistance to acceleration. The variable a denotes acceleration, which is defined as the rate of change of velocity. Therefore, the correct matching is: 1-c, 2-d, 3-a, 4-b

❓ Why Other Options Are Incorrect

�� Option A → Physical meanings of acceleration and force are incorrect.
�� Option B → Multiple quantities are incorrectly matched.
�� Option C → Force and inertia terms are interchanged.

🎯 Strategy

Used – Formula Recall

Application
Interpret each symbol and term appearing in
a=-eE/m
Final Logic
Match every symbol with its physical significance in the acceleration equation.

🧠 Memory Trick

a → Velocity Change

📚 Class: XII | Book: NCERT Physics Part II | Chapter: Current Electricity | Topic: Acceleration Mechanism | Subtopic: Electron Mass and Charge

6 In the conceptual setup with charged discs at the ends of a cylinder, if fresh charges are continuously supplied to the ends

A Electrons will instantly cease moving once the initial, localized neutralization is complete.

B A steady electric field is maintained in the body, resulting in a continuous steady current.

C The heavy positive ions will physically detach and drift towards the negative disc.

D The internal thermal motion of the electrons becomes entirely unidirectional and ordered.

💡 Short Explanation

�� Continuous charge replenishment maintains the electric field. �� The maintained field produces continuous drift. �� Continuous drift results in steady current.

✅ Correct Answer Explanation

When opposite charges are placed at the ends of a conductor, an electric field is established inside it. Initially, electrons drift and gradually neutralize the charge imbalance. If no further charges are supplied, the electric field disappears and the current stops. However, if an external source such as a battery continuously replenishes charges at the ends, the electric field remains constant throughout the conductor. Electrons continue to experience an electric force and acquire a steady drift velocity. Although individual electrons undergo random thermal motion and collisions, the average drift remains constant, producing a steady electric current. Therefore, a continuous supply of charges is the mechanism by which batteries maintain current in electrical circuits.

❓ Why Other Options Are Incorrect

�� Option A → Continuous replenishment prevents current from stopping.
�� Option C → Positive ions remain fixed in the metallic lattice.
�� Option D → Thermal motion remains random even during current flow.

🎯 Strategy

Used – Concept Application

Application
Apply the role of a battery in maintaining an electric field.
Final Logic
Continuous charge replenishment maintains the field and therefore maintains steady current.

🧠 Memory Trick

Drift → Steady Current

📚 Class: XII | Book: NCERT Physics Part II | Chapter: Current Electricity | Topic: Acceleration Mechanism | Subtopic: Field Force Effect

7 Correct statements regarding the elapsed time t_i parameter
Statements:
1. It governs the magnitude of the velocity an electron has gained from the electric field since its last collision.
2. It represents the time elapsed since the precise last collision for the i^(th)individual electron.
3. It varies randomly across the electron population at a given instant t.
4. It is perfectly identical to the relaxation time τfor all electrons simultaneously.

A 1, 2 and 4 are correct

B 1, 2 and 3 are correct

C 1, 3 and 4 are correct

D 2, 3 and 4 are correct

💡 Short Explanation

�� t_i measures time since the last collision. �� Different electrons have different values of t_i. �� Larger t_i means greater field-induced velocity gain.

✅ Correct Answer Explanation

In the microscopic theory of conduction, t_i denotes the time elapsed since the last collision of the i^(th)electron. Because collisions occur randomly, different electrons have different elapsed times at any instant. The field-induced velocity gained by an electron is -eE/mt_i showing that the velocity acquired from the electric field depends directly on t_i. Since collisions occur at random intervals, the values of t_i vary throughout the electron population. The relaxation time τis only the average value of all such times and is not identical to every individual t_i.

❓ Why Other Options Are Incorrect

�� Option A → Statement 4 is incorrect.
�� Option C → Statement 4 is incorrect.
�� Option D → Statement 4 is incorrect.

🎯 Strategy

Used – Concept Application

Application
Differentiate between individual collision times and average relaxation time.
Final Logic
t_i varies from electron to electron, whereas τis only the average.

🧠 Memory Trick

τ→ Average Time

📚 Class: XII | Book: NCERT Physics Part II | Chapter: Current Electricity | Topic: Time Parameters | Subtopic: Elapsed Time t_i

8 By mathematically relating the resistivity ρto the macroscopic collision parameters, substituting σ=1/ρinto the conductivity formula gives the relaxation time τwhich will be

A m/ne^2ρ

B ne^2/mρ

C ρm/ne^2

D ne^2ρ/m

💡 Short Explanation

�� Conductivity and resistivity are reciprocals. �� Conductivity depends on relaxation time. �� Rearranging gives the expression for τ.

✅ Correct Answer Explanation

The conductivity of a conductor is σ=ne^2τ/m and resistivity is related by ρ=1/σ Substituting, 1/ρ=ne^2τ/m Rearranging, τ=m/ne^2ρ Thus the relaxation time depends directly on electron mass and inversely on electron density, electronic charge squared, and resistivity.

❓ Why Other Options Are Incorrect

�� Option B → Incorrect algebraic rearrangement.
�� Option C → Places ρin the numerator incorrectly.
�� Option D → Dimensionally incorrect.

🎯 Strategy

Used – Formula Recall

Application
Use conductivity and resistivity relations.
Final Logic
σ=ne^2τ/mandσ=1/ρ
lead directly to
τ=m/ne^2ρ

🧠 Memory Trick

Resistivity Up → Relaxation Time Down

📚 Class: XII | Book: NCERT Physics Part II | Chapter: Current Electricity | Topic: Time Parameters | Subtopic: Relaxation Time

9 Nature of the individual components v_i and the field-induced term
-eEt_i/m
inside the instantaneous velocity equation
V_i=v_i-eEt_i/m
is:

A Directional, Directional

B Directional, Random

C Random, Random

D Random, Directional

💡 Short Explanation

�� v_i is the random thermal velocity after the last collision. �� -eEt_i/m is produced by the electric field. �� The field-induced term has a definite direction.

✅ Correct Answer Explanation

The instantaneous velocity of the i^(th)electron is given by V_i=v_i-eEt_i/m Here, v_i represents the random thermal velocity of the electron immediately after its last collision with a positive ion. Because collisions occur randomly, both the magnitude and direction of v_i are random. The term -eEt_i/m represents the velocity gained due to acceleration by the applied electric field during the time interval t_i. Since the electric field has a fixed direction, this contribution is directional. The negative sign indicates that the electron velocity gained due to the field is opposite to the direction of the electric field. Therefore, v_i is random while -eEt_i/m is directional.

❓ Why Other Options Are Incorrect

�� Option A → The thermal velocity component is random.
�� Option B → Reverses the nature of the two terms.
�� Option C → The field-induced term is not random.

🎯 Strategy

Used – Concept Application

Application
Identify the physical meaning of each term in the instantaneous velocity equation.
Final Logic
Thermal motion is random, whereas the electric field produces a directed velocity component.

🧠 Memory Trick

eEt_i/m→ Electric Field → Directional

📚 Class: XII | Book: NCERT Physics Part II | Chapter: Current Electricity | Topic: Drift Velocity Formula | Subtopic: Instantaneous Velocity

10 If a conductive material has an internal relaxation time of 3.0×10^(-14)s and an applied steady field of 0.5 V/m, the magnitude of the drift velocity (using e/m≈1.76×10^(11)C/kg) will be

A 2.64×10^(-3)m/s

B 3.15×10^(-2)m/s

C 1.85×10^(-4)m/s

D 5.20×10^(-3)m/s

💡 Short Explanation

�� Drift velocity depends on E and τ. �� Use v_d=eEτ/m. �� Substitute the given values.

✅ Correct Answer Explanation

The magnitude of drift velocity is v_d=eEτ/m Substituting the given values, v_d=(1.76×10^(11))(0.5)(3.0×10^(-14))v_d=2.64×10^(-3) m/s Thus the electrons drift with a very small average speed even though their thermal speeds are much larger.

❓ Why Other Options Are Incorrect

�� Option B → Arithmetic error.
�� Option C → Incorrect power of ten.
�� Option D → Incorrect multiplication.

🎯 Strategy

Used – Substitution

Application
Substitute the given values into the drift velocity formula.
Final Logic
v_d=eEτ/m=(1.76×10^(11))(0.5)(3×10^(-14))=2.64×10^(-3) m/s

🧠 Memory Trick

Stronger Field → Larger Drift

📚 Class: XII | Book: NCERT Physics Part II | Chapter: Current Electricity | Topic: Drift Velocity Formula | Subtopic: Average Drift Result

11 Which of the following statements is correct regarding the steady drift speed of electrons in a conductor?
Statements:
1. Electrons continuously accelerate between collisions, but their macroscopic average remains steady.
2. The average macroscopic drift velocity vector remains independent of time.
3. The steady drift physically implies that the instantaneous acceleration of individual free electrons is zero.
4. The steady average speed is attained strictly because the kinetic energy is converted into mass.

A 1, 2 and 4 are correct

B 1 and 2 are correct

C 3 and 4 are correct

D 1, 2 and 3 are correct

💡 Short Explanation

�� Individual electrons accelerate between collisions. �� Frequent collisions maintain a constant average drift speed. �� Steady drift does not imply zero acceleration.

✅ Correct Answer Explanation

When an electric field is applied, electrons experience a force and accelerate between successive collisions. However, collisions repeatedly randomize their motion, preventing indefinite acceleration. As a result, the average drift velocity reaches a constant value known as the steady drift velocity. The macroscopic drift velocity remains constant with time for a steady current even though individual electrons continuously accelerate between collisions. Therefore, statements 1 and 2 are correct. Statement 3 is incorrect because electrons do accelerate between collisions. Statement 4 is incorrect because steady drift has nothing to do with conversion of kinetic energy into mass.

❓ Why Other Options Are Incorrect

�� Option A → Statement 4 is incorrect.
�� Option C → Statements 3 and 4 are incorrect.
�� Option D → Statement 3 is incorrect.

🎯 Strategy

Used – Concept Application

Application
Distinguish between microscopic electron motion and macroscopic current behavior.
Final Logic
Individual electrons accelerate, but the average drift velocity remains constant.

🧠 Memory Trick

Average Drift → Constant

📚 Class: XII | Book: NCERT Physics Part II | Chapter: Current Electricity | Topic: Drift Characteristics | Subtopic: Steady Average Speed

12 Incorrect statement linking drift direction to the applied electric parameters

A The current density vector j is parallel to the electric field vector E.

B Electrons physically drift from a region of lower electric potential to a region of higher potential.

C The drift velocity vector is precisely parallel to the applied electric field.

D The defining negative sign in the drift velocity equation inherently indicates opposite alignment to E.

💡 Short Explanation

�� Electrons are negatively charged. �� Drift velocity is opposite to the electric field. �� Current density is parallel to the electric field.

✅ Correct Answer Explanation

The drift velocity of electrons is given by v_d=-eτ/mE The negative sign indicates that electrons drift opposite to the electric field direction. Therefore, statement C is incorrect. Since conventional current is defined in the direction of positive charge flow, the current density vector is parallel to the electric field. Electrons move from lower potential to higher potential because they carry negative charge. Thus statements A, B, and D are correct while statement C is incorrect.

❓ Why Other Options Are Incorrect

�� Option A → Correct relation for current density.
�� Option B → Correct direction of electron drift.
�� Option D → Correct interpretation of the negative sign.

🎯 Strategy

Used – Formula Recall

Application
Use the drift velocity equation and sign convention.
Final Logic
Negative charge causes electron drift opposite to the electric field.

🧠 Memory Trick

Current Follows Field

📚 Class: XII | Book: NCERT Physics Part II | Chapter: Current Electricity | Topic: Drift Characteristics | Subtopic: Field Direction Relation

13 The core physical significance of the immense number density parameter (n, 10^(29) m^(-3))is that

A It causes the individual thermal speeds to become completely indistinguishable and small.

B It totally prevents any free electrons from accelerating under intense voltages.

C It allows an extremely small individual drift speed to collectively yield a substantial macroscopic current.

D It restricts the mathematical validity of Ohm's law to highly resistive insulators.

💡 Short Explanation

�� Electron density is extremely large. �� Drift speed is very small. �� Large numbers of carriers produce large current.

✅ Correct Answer Explanation

For a conductor, I=neA∣v_d∣ where n is the number density of free electrons. In metals, n is typically of the order of 10^(28)–10^(29) m^(-3). Although the drift velocity v_d is very small (often around 10^(-4)to 10^(-3) m/s), the enormous number of free electrons ensures that a large amount of charge crosses any cross-section every second. This results in measurable macroscopic currents. Therefore, the significance of large n is that it compensates for the tiny drift speed.

❓ Why Other Options Are Incorrect

�� Option A → Thermal speed is not determined by number density.
�� Option B → Electrons can still accelerate under electric fields.
�� Option D → Ohm's law is not restricted to insulators.

🎯 Strategy

Used – Concept Application

Application
Analyze the microscopic current equation.
Final Logic
Large carrier density × Small drift speed = Significant current.

🧠 Memory Trick

Tiny Drift × Huge Number = Big Current

📚 Class: XII | Book: NCERT Physics Part II | Chapter: Current Electricity | Topic: Charge Transport | Subtopic: Volume Charge Carriers

14 In analytically defining the net current across a planar area A via the drift velocity, the expression
-neA∣v_d∣Δt

A Conceptually equates to zero because the random thermal motion flawlessly cancels it out.

B Calculates the total charge transported to the right, equating to the negative of the charge flowing parallel to E.

C Intrinsically represents the total positive charge moving strictly in the identical direction of the field.

D Is functionally valid only when the cross-sectional area A is perfectly parallel to the electric field lines.

💡 Short Explanation

�� Expression represents transported electron charge. �� Negative sign arises from electron charge. �� Current direction is opposite to electron motion.

✅ Correct Answer Explanation

During a small interval Δt, electrons drift a distance ∣v_d∣Δt. The number of electrons crossing area A is nA∣v_d∣Δt Since each electron carries charge -e, ΔQ=-neA∣v_d∣Δt This expression represents the charge transported by electrons. Because electrons move opposite to the electric field, the corresponding conventional current is along the electric field direction. Hence Option B is correct.

❓ Why Other Options Are Incorrect

�� Option A → Drift current is not cancelled by thermal motion.
�� Option C → Expression refers to electron charge, not positive charges.
�� Option D → No such restriction exists.

🎯 Strategy

Used – Concept Application

Application
Apply the microscopic definition of current.
Final Logic
Charge transported equals number of carriers × charge per carrier.

🧠 Memory Trick

Electron Charge → Negative Sign

📚 Class: XII | Book: NCERT Physics Part II | Chapter: Current Electricity | Topic: Charge Transport | Subtopic: Infinitesimal Charge Flow

15 Match List I with List II regarding Current Density and Electric Current

List I	List II
1. SI Unit of current density j	a. (ne
2. j×A	b. Parallel to vector E
3. Magnitude ( — j 4. jvector direction	d. A/m²

A 1-a, 2-d, 3-c, 4-b

B 1-c, 2-a, 3-d, 4-b

C 1-d, 2-c, 3-a, 4-b

D 1-b, 2-c, 3-a, 4-d

💡 Short Explanation

�� Current density is current per unit area. �� Its magnitude depends on carrier density and drift velocity. �� Current density is directed along the electric field.

✅ Correct Answer Explanation

Current density is defined as j=I/A where I is the electric current and A is the cross-sectional area. The magnitude of current density is ∣j∣=ne∣v_d∣ where n is the number density of free charge carriers, e is the electronic charge, and v_d is the drift velocity. The SI unit of current density is A/m^2 For a conductor obeying Ohm's law, the current density vector is parallel to the electric field vector E. Also, I=jA Therefore, the correct matching is: 1-d, 2-c, 3-a, 4-b

❓ Why Other Options Are Incorrect

�� Option A → Magnitude and unit are interchanged.
�� Option B → Unit and current relations are mismatched.
�� Option D → Direction and unit are incorrectly matched.

🎯 Strategy

Used – Formula Recall

Application
Recall the standard definitions of current density, drift velocity, and electric current.
Final Logic
j=I/A,∣j∣=ne∣v_d∣,I=jA
and the SI unit of j is A/m².

🧠 Memory Trick

j follows E

📚 Class: XII | Book: NCERT Physics Part II | Chapter: Current Electricity | Topic: Microscopic Current | Subtopic: Current Density Magnitude

16 By equating the derived microscopic equation
j=(ne^2τ/m)E
with the macroscopic Ohm's law form
j=σE
the conductivity σof a material is

A m/ne^2τ

B ne^2τ/m

C neτ/m

D ne^2/mτ

💡 Short Explanation

�� Current density is proportional to electric field. �� Conductivity is the proportionality constant. �� Compare microscopic and macroscopic forms of Ohm's law.

✅ Correct Answer Explanation

The microscopic form of Ohm's law is j=(ne^2τ/m)E where n is the number density of free electrons, e is the electronic charge, τis the relaxation time, and m is the mass of an electron. The macroscopic form of Ohm's law is j=σE Comparing the coefficients of E, σ=ne^2τ/m Thus conductivity increases with carrier density and relaxation time and decreases with electron mass.

❓ Why Other Options Are Incorrect

�� Option A → Represents resistivity-related form.
�� Option C → Missing one factor of e.
�� Option D → Relaxation time incorrectly placed in denominator.

🎯 Strategy

Used – Formula Recall

Application
Compare microscopic and macroscopic forms of Ohm's law.
Final Logic
j=(ne^2τ/m)E=σE
Therefore,
σ=ne^2τ/m

🧠 Memory Trick

Conductivity = Carriers × Charge² × Relaxation Time ÷ Mass

📚 Class: XII | Book: NCERT Physics Part II | Chapter: Current Electricity | Topic: Microscopic Current | Subtopic: Electronic Conductivity

17 Correct statements about carrier mobility μ
Statements:
1. It is an important parameter in defining conductivity derived from mobile charge carriers.
2. It is defined as the magnitude of drift velocity per unit electric field.
3. It can be mathematically expressed as eτ/m for free electrons.
4. It is formally treated as a negative quantity for negatively charged electrons.

A 1, 2 and 4 are correct

B 1, 3 and 4 are correct

C 2, 3 and 4 are correct

D 1, 2 and 3 are correct

💡 Short Explanation

�� Mobility measures ease of carrier motion. �� Mobility relates drift velocity and electric field. �� Mobility contributes directly to conductivity.

✅ Correct Answer Explanation

Carrier mobility is defined as μ=∣v_d∣/E which represents the drift velocity acquired per unit electric field. Using the drift velocity relation v_d=eEτ/m we obtain μ=eτ/m for free electrons. Conductivity can also be written as σ=neμ showing the direct role of mobility in electrical conduction. Mobility is treated as a positive physical parameter representing magnitude. Therefore statement 4 is incorrect.

❓ Why Other Options Are Incorrect

�� Option A → Statement 4 is incorrect.
�� Option B → Statement 4 is incorrect.
�� Option C → Statement 4 is incorrect.

🎯 Strategy

Used – Concept Application

Application
Use the definitions of drift velocity, mobility, and conductivity.
Final Logic
μ=∣v_d∣/E=eτ/m
and
σ=neμ

🧠 Memory Trick

Conductivity = Carrier Density × Charge × Mobility

📚 Class: XII | Book: NCERT Physics Part II | Chapter: Current Electricity | Topic: Carrier Mobility | Subtopic: Definition of Mobility

18 If mobility is given as
4.5×10^3 cm^2/(V s)
its value in SI units is

A 0.45 m^2/(V s)

B 4.5×10^(-2) m^2/(V s)

C 4.5 m^2/(V s)

D 45 m^2/(V s)

💡 Short Explanation

�� 1 cm^2=10^(-4) m^2 �� Convert area units carefully. �� Multiply by 10^(-4).

✅ Correct Answer Explanation

Given, μ=4.5×10^3 cm^2/(V s) Since 1 cm^2=10^(-4) m^2 we get μ=(4.5×10^3)(10^(-4))μ=4.5×10^(-1)μ=0.45 m^2/(V s) Therefore Option A is correct.

❓ Why Other Options Are Incorrect

�� Option B → Incorrect power of ten.
�� Option C → Conversion factor applied incorrectly.
�� Option D → Unit conversion error.

🎯 Strategy

Used – Unit Conversion

Application
Convert square centimetres into square metres.
Final Logic
4.5×10^3×10^(-4)=0.45

🧠 Memory Trick

cm² → m² ⇒ Multiply by 10^(-4)

📚 Class: XII | Book: NCERT Physics Part II | Chapter: Current Electricity | Topic: Carrier Mobility | Subtopic: SI Units of Mobility

19 Incorrect statement regarding the estimation of electron density parameter in copper

A The overall density calculation relies on the atomic mass of copper being approximately 63.5 u.

B The mass of one cubic metre of copper is approximately 9.0×10^3 kg.

C Only a tiny fraction of copper atoms contribute a conduction electron, heavily explaining the low drift speed.

D Avogadro's number 6.0×10^(23)copper atoms corresponds to 63.5 g.

💡 Short Explanation

�� Most copper atoms contribute conduction electrons. �� Electron density in copper is extremely large. �� Drift speed is small despite many free electrons.

✅ Correct Answer Explanation

Copper is an excellent conductor because a large number of its atoms contribute free electrons for conduction. The electron number density is of the order of 10^(29) m^(-3) and not a tiny fraction as stated in Option C. The commonly used values in estimating electron density are: • Density of copper ≈ 9.0×10^3 kg/m^3 • Atomic mass ≈ 63.5 g/mol • Avogadro number ≈ 6.0×10^(23) These values allow calculation of the number of atoms and hence the number of free electrons per unit volume.

❓ Why Other Options Are Incorrect

�� Option A → Correct numerical value.
�� Option B → Correct density approximation.
�� Option D → Correct Avogadro relation.

🎯 Strategy

Used – Concept Application

Application
Use the free-electron model of metallic conduction.
Final Logic
Copper contains an enormous density of conduction electrons.

🧠 Memory Trick

Huge Density + Tiny Drift = Large Current

📚 Class: XII | Book: NCERT Physics Part II | Chapter: Current Electricity | Topic: Electron Scales | Subtopic: Copper Atom Contribution

20 Thermal speed vs Drift speed vs Field propagation speed in a typical conductor

A High, Extremely Low, Speed of Light

B Low, High, Speed of Light

C High, Low, Speed of Sound

D Speed of Light, Low, High

💡 Short Explanation

�� Thermal speed is very large. �� Drift speed is extremely small. �� Electrical signals propagate nearly at light speed.

✅ Correct Answer Explanation

Free electrons inside a conductor possess large random thermal speeds, typically hundreds of metres per second or more. However, when an electric field is applied, the resulting drift speed is extremely small, usually of the order of 10^(-4) to 10^(-3) m/s Despite this small drift velocity, electrical effects appear almost instantaneously because the electric field propagates through the conductor at a speed close to 3×10^8 m/s which is approximately the speed of light. Therefore, the correct order is: Thermal Speed → High Drift Speed → Extremely Low Field Propagation Speed → Speed of Light

❓ Why Other Options Are Incorrect

�� Option B → Thermal and drift speeds reversed.
�� Option C → Field propagation is not limited to the speed of sound.
�� Option D → Thermal speed is not equal to light speed.

🎯 Strategy

Used – NCERT Recall

Application
Recall the characteristic orders of magnitude of important speeds in conductors.
Final Logic
Thermal Speed ≫ Drift Speed, while Field Propagation ≈ Speed of Light.

🧠 Memory Trick

Field → Light Speed

📚 Class: XII | Book: NCERT Physics Part II | Chapter: Current Electricity | Topic: Electron Scales | Subtopic: Thermal vs Drift Speed Ratio

CUET UG Physics Booster Test – 3 Electron Dynamics and Drift

CUET UG Physics Booster Test - 3 Electron Dynamics and Drift

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