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Current Electricity

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Chapter Notes

Overview
This chapter builds on electrostatics to study charges in motion, i.e., electric current. It introduces the fundamental laws governing steady currents, including Ohm's law, the origin of resistivity, and the concepts of emf and internal resistance. The one big idea a student must walk away with is that electric current in conductors is a drift of electrons, and the resistance to this flow is explained by collisions with ions, leading to power dissipation and the need for Kirchhoff's rules to analyze complex circuits.
Key Concepts (14)
Electric Current
The net amount of charge flowing across a cross-section of a conductor per unit time. For steady current, I = q/t; more generally, I = dQ/dt.
e.g. When you switch on a torch, the flow of charges through the bulb constitutes an electric current of about 0.3 A.
Ohm's Law
At constant temperature, the potential difference across the ends of a conductor is directly proportional to the current flowing through it, i.e., V ∝ I, or V = IR.
e.g. A 10 Ω resistor connected to a 5 V battery will draw a current of 0.5 A.
Resistance
The property of a conductor that opposes the flow of current, given by R = V/I. Its SI unit is ohm (Ω).
e.g. A thin, long wire has higher resistance than a thick, short wire of the same material.
Resistivity
The intrinsic property of a material that quantifies how strongly it opposes the flow of electric current, given by ρ = RA/l. Its SI unit is ohm-meter (Ωm).
e.g. Copper has low resistivity (1.7 × 10⁻⁸ Ωm), making it a good conductor, while rubber has very high resistivity, making it an insulator.
Conductivity
The reciprocal of resistivity, σ = 1/ρ. It measures how easily a material allows the flow of electric current. SI unit is siemens per meter (S/m).
e.g. Metals have high conductivity, while insulators have very low conductivity.
Drift Velocity
The average constant velocity acquired by free electrons in a conductor under the influence of an electric field, given by vd = (eEτ)/m.
e.g. In a copper wire carrying 1.5 A current, the drift velocity is only about 1.1 mm/s, much smaller than the random thermal speeds.
Relaxation Time
The average time between successive collisions of an electron with the ions in a conductor, denoted by τ.
e.g. For copper at room temperature, τ is of the order of 10⁻¹⁴ s.
Mobility
The magnitude of drift velocity per unit electric field, μ = |vd|/E. Its SI unit is m²/Vs.
e.g. Electrons in a metal have higher mobility than ions in an electrolyte.
Electromotive Force (emf)
The potential difference between the positive and negative electrodes of a cell when no current is flowing through the circuit (open circuit). It is denoted by ε.
e.g. A fresh AA battery has an emf of 1.5 V.
Internal Resistance
The resistance offered by the electrolyte and electrodes of a cell to the flow of current through it, denoted by r.
e.g. A dry cell has a higher internal resistance (a few ohms) than a lead-acid car battery (fractions of an ohm).
Temperature Coefficient of Resistivity
The fractional change in resistivity per degree change in temperature, given by α = (ρT - ρ0) / [ρ0 (T - T0)]. Its unit is °C⁻¹ or K⁻¹.
e.g. For copper, α is positive (about 0.004/°C), meaning its resistivity increases with temperature.
Current Density
The current per unit area of cross-section taken normal to the current, j = I/A. It is a vector quantity directed along E. SI unit is A/m².
e.g. If 2 A flows through a wire of cross-sectional area 1 mm², the current density is 2 × 10⁶ A/m².
Kirchhoff's Junction Rule
At any junction in an electrical circuit, the sum of currents entering the junction is equal to the sum of currents leaving the junction.
e.g. In a circuit, if 3 A enters a junction and 1 A leaves through one branch, then 2 A must leave through the other branch.
Kirchhoff's Loop Rule
The algebraic sum of changes in potential around any closed loop in a circuit is zero.
e.g. In a simple loop with a 10 V battery and two 2 Ω resistors, the sum of voltage drops (IR) equals the battery emf.
Formulas & Equations (16)
I = q/t
Reads as: Current equals charge divided by time
Variables: I = current (A), q = net charge flowing (C), t = time interval (s)
Use when: Calculating steady current when charge and time are given.
⚠ Using total charge instead of net charge; forgetting that current is due to net charge flow.
I = dQ/dt
Reads as: Current is the instantaneous rate of flow of charge
Variables: I = current (A), dQ = infinitesimal charge (C), dt = infinitesimal time (s)
Use when: Defining current for non-steady or time-varying currents.
⚠ Confusing this with average current formula.
V = IR
Reads as: Voltage equals current times resistance
Variables: V = potential difference (V), I = current (A), R = resistance (Ω)
Use when: Applying Ohm's law to find voltage, current, or resistance in a conductor.
⚠ Applying it to non-ohmic devices like diodes without checking linearity.
R = ρ l / A
Reads as: Resistance equals resistivity times length divided by area
Variables: R = resistance (Ω), ρ = resistivity (Ωm), l = length (m), A = cross-sectional area (m²)
Use when: Calculating resistance of a conductor given its dimensions and material.
⚠ Forgetting to convert area to m²; using diameter instead of radius for circular wires.
E = ρ j
Reads as: Electric field equals resistivity times current density
Variables: E = electric field (V/m), ρ = resistivity (Ωm), j = current density (A/m²)
Use when: Relating electric field inside a conductor to current density.
⚠ Writing j = ρ E instead of j = σ E or E = ρ j.
j = σ E
Reads as: Current density equals conductivity times electric field
Variables: j = current density (A/m²), σ = conductivity (S/m), E = electric field (V/m)
Use when: Expressing Ohm's law in vector form.
⚠ Confusing σ with ρ.
vd = (eEτ)/m
Reads as: Drift velocity equals electron charge times electric field times relaxation time divided by electron mass
Variables: vd = drift velocity (m/s), e = charge of electron (1.6 × 10⁻¹⁹ C), E = electric field (V/m), τ = relaxation time (s), m = mass of electron (9.1 × 10⁻³¹ kg)
Use when: Calculating drift velocity from microscopic parameters.
⚠ Forgetting the negative sign; using mass of the ion instead of electron.
I = n e A vd
Reads as: Current equals number density times electron charge times area times drift velocity
Variables: I = current (A), n = number of free electrons per unit volume (m⁻³), e = electron charge (C), A = cross-sectional area (m²), vd = drift velocity (m/s)
Use when: Relating macroscopic current to microscopic drift velocity.
⚠ Using n as number of atoms instead of free electrons per unit volume.
σ = n e² τ / m
Reads as: Conductivity equals number density times electron charge squared times relaxation time divided by mass
Variables: σ = conductivity (S/m), n = free electron density (m⁻³), e = electron charge (C), τ = relaxation time (s), m = electron mass (kg)
Use when: Deriving conductivity from microscopic properties.
⚠ Forgetting the square on e.
μ = |vd| / E
Reads as: Mobility equals magnitude of drift velocity divided by electric field
Variables: μ = mobility (m²/Vs), vd = drift velocity (m/s), E = electric field (V/m)
Use when: Calculating mobility of charge carriers.
⚠ Using vd without absolute value; mobility is always positive.
ρT = ρ0 [1 + α (T - T0)]
Reads as: Resistivity at temperature T equals resistivity at reference temperature times one plus alpha times temperature difference
Variables: ρT = resistivity at T (Ωm), ρ0 = resistivity at T0 (Ωm), α = temperature coefficient of resistivity (°C⁻¹), T = final temperature (°C), T0 = reference temperature (°C)
Use when: Calculating resistivity change with temperature over a limited range.
⚠ Using this formula for semiconductors where α is negative and the relation is not linear.
P = V I = I² R = V² / R
Reads as: Power equals voltage times current, also equals current squared times resistance, also equals voltage squared divided by resistance
Variables: P = power (W), V = potential difference (V), I = current (A), R = resistance (Ω)
Use when: Calculating power dissipated in a resistor or delivered by a source.
⚠ Using P = V²/R for a non-ohmic device; forgetting that V is the voltage across the resistor, not the source emf.
V = ε - I r
Reads as: Terminal voltage equals emf minus current times internal resistance
Variables: V = terminal voltage (V), ε = emf (V), I = current (A), r = internal resistance (Ω)
Use when: Finding the potential difference across the terminals of a cell when current is drawn.
⚠ Using V = ε + I r when current flows from positive to negative inside the cell; sign convention is crucial.
I = ε / (R + r)
Reads as: Current equals emf divided by sum of external and internal resistances
Variables: I = current (A), ε = emf (V), R = external resistance (Ω), r = internal resistance (Ω)
Use when: Calculating current in a simple circuit with a cell and external resistor.
⚠ Forgetting to include internal resistance r in the denominator.
For series combination of cells: εeq = ε1 + ε2 + ... ; req = r1 + r2 + ...
Reads as: Equivalent emf is the sum of individual emfs; equivalent internal resistance is the sum of individual internal resistances
Variables: εeq = equivalent emf (V), ε1, ε2 = emf of individual cells (V), req = equivalent internal resistance (Ω), r1, r2 = internal resistances (Ω)
Use when: Replacing a series combination of cells with a single equivalent cell.
⚠ Adding emfs with wrong sign if cells are connected with opposite polarity.
For parallel combination of cells: 1/req = 1/r1 + 1/r2 + ... ; εeq/req = ε1/r1 + ε2/r2 + ...
Reads as: Reciprocal of equivalent internal resistance equals sum of reciprocals; equivalent emf divided by equivalent resistance equals sum of each emf divided by its internal resistance
Variables: req = equivalent internal resistance (Ω), r1, r2 = internal resistances (Ω), εeq = equivalent emf (V), ε1, ε2 = emf of cells (V)
Use when: Replacing a parallel combination of cells with a single equivalent cell.
⚠ Assuming εeq is simply the average of ε1 and ε2; using the formula only when cells are identical.
How It Works
Origin of Resistivity (Drift of Electrons)
  1. In the absence of an electric field, electrons move randomly with zero average velocity due to thermal motion and collisions with fixed ions.
  2. When an electric field E is applied, each electron experiences a force -eE and accelerates between collisions.
  3. After each collision, the electron's velocity is randomized, but it gains a small net drift in the direction opposite to E.
  4. The average time between collisions is the relaxation time τ.
  5. The drift velocity vd = (eEτ)/m is derived by averaging the velocities of all electrons.
  6. The current density j = n e vd leads to j = (n e² τ / m) E, which is Ohm's law with conductivity σ = n e² τ / m.
💡 Drift velocity is very small (mm/s) compared to random thermal speeds (10⁵ m/s); current is large due to enormous electron density (~10²⁸ m⁻³).
Temperature Dependence of Resistivity
  1. As temperature increases, the average speed of electrons increases, leading to more frequent collisions with ions.
  2. This decreases the relaxation time τ.
  3. For metals, n (free electron density) is nearly independent of temperature, so resistivity ρ ∝ 1/τ increases with temperature.
  4. For semiconductors, n increases significantly with temperature, more than compensating the decrease in τ, so resistivity decreases with temperature.
  5. Over a limited range, metallic resistivity follows ρT = ρ0 [1 + α (T - T0)] with α positive.
💡 For metals, α is positive; for semiconductors, α is negative. Alloys like nichrome have very small α, making them suitable for standard resistors.
Working of a Cell (emf and Internal Resistance)
  1. A cell has two electrodes (positive P and negative N) immersed in an electrolyte.
  2. Chemical reactions create a potential difference between the electrodes and the electrolyte: V+ at P and -V- at N.
  3. With no current (open circuit), the terminal voltage equals the emf ε = V+ + V-.
  4. When current flows, the electrolyte offers internal resistance r, causing a voltage drop Ir inside the cell.
  5. The terminal voltage becomes V = ε - Ir.
  6. The current in the external circuit is I = ε / (R + r).
💡 Emf is the open-circuit voltage; internal resistance causes the terminal voltage to drop when current is drawn.
Application of Kirchhoff's Rules
  1. Label all currents in each branch with an assumed direction.
  2. Apply the junction rule at any node: sum of currents entering = sum of currents leaving.
  3. Choose closed loops in the circuit.
  4. Apply the loop rule: the algebraic sum of potential changes (IR drops and emf rises) around any closed loop is zero.
  5. Solve the resulting simultaneous equations for unknown currents.
  6. If a calculated current is negative, its actual direction is opposite to the assumed direction.
💡 The loop rule is a consequence of conservation of energy; the junction rule is a consequence of conservation of charge. Always define a sign convention for voltage drops and rises before applying the loop rule.
Exam Traps — Don't Make These Mistakes
⚠ Confusing emf with terminal voltage
✗ The emf of a cell is the voltage across its terminals when current is flowing.
→ Emf is the open-circuit voltage (no current). Terminal voltage V = ε - Ir is less than emf when current flows due to internal resistance drop.
✓ Emf is the potential difference between the terminals of a cell when no current is drawn from it (open circuit).
⚠ Applying Ohm's law to non-ohmic devices
✗ V = IR always holds for any electrical component.
→ Ohm's law is valid only for ohmic conductors where V ∝ I. Devices like diodes, semiconductors, and electrolytes show non-linear V-I characteristics.
✓ Ohm's law is obeyed by metallic conductors at constant temperature; it does not hold for non-ohmic materials like diodes.
⚠ Incorrect sign in loop rule for cells
✗ When going from negative to positive terminal of a cell, the potential change is -ε.
→ Going from negative to positive terminal means moving to a higher potential, so the change is +ε. The sign depends on the direction of traversal relative to the cell's polarity.
✓ When traversing a loop from the negative to the positive terminal of a cell, the potential change is +ε; from positive to negative, it is -ε.
⚠ Forgetting internal resistance in circuit calculations
✗ The current in a circuit with a cell of emf 10 V and external resistance 5 Ω is I = 10/5 = 2 A.
→ The total resistance in the circuit is R + r, where r is the internal resistance of the cell. Ignoring r gives an overestimated current.
✓ The current is I = ε / (R + r), where r is the internal resistance of the cell.
⚠ Misinterpreting drift velocity direction
✗ Electrons drift in the direction of the electric field.
→ Electrons are negatively charged, so they experience a force opposite to the electric field direction. Thus, they drift opposite to E.
✓ Electrons drift in a direction opposite to the applied electric field, i.e., from lower to higher potential.
⚠ Using series formula for parallel cells incorrectly
✗ For two cells in parallel, εeq = ε1 + ε2 and req = r1 + r2.
→ That is the formula for series combination. For parallel, 1/req = 1/r1 + 1/r2 and εeq/req = ε1/r1 + ε2/r2.
✓ For parallel combination, the equivalent internal resistance is given by 1/req = 1/r1 + 1/r2, and the equivalent emf is εeq = (ε1/r1 + ε2/r2) × req.
Compare & Contrast
Definition and condition
Emf (ε)
Terminal Voltage (V)
Emf is the potential difference across the terminals of a cell when no current flows (open circuit), while terminal voltage is the potential difference when current is being drawn (closed circuit). V = ε - Ir.
Dependence on dimensions
Resistivity (ρ)
Resistance (R)
Resistivity is an intrinsic property of the material and is independent of the conductor's dimensions, whereas resistance depends on the material's resistivity, length, and cross-sectional area (R = ρl/A).
Equivalent emf and internal resistance
Series Combination of Cells
Parallel Combination of Cells
In series, εeq = ε1 + ε2 + ... and req = r1 + r2 + ...; in parallel, 1/req = 1/r1 + 1/r2 + ... and εeq/req = ε1/r1 + ε2/r2 + ...
Exam Focus
Marks pattern: Typically 2-3 MCQs (1 mark each), 1 short answer question (2-3 marks) on drift velocity or resistivity, 1 numerical (3 marks) on combination of cells or Kirchhoff's rules, and 1 long answer (5 marks) on circuit analysis using Kirchhoff's rules or derivation of Ohm's law from drift velocity.
Most asked: Ohm's law and its limitations · Drift velocity and its relation with current · Temperature dependence of resistivity · Combination of cells (series and parallel) · Kirchhoff's rules and their application to complex circuits · Power dissipation in resistors
Don't skip: Numerical problems involving Kirchhoff's rules to find currents in a multi-loop circuit.; Derivation of Ohm's law from the drift velocity model.; Problems on series and parallel combinations of cells with internal resistance.
One-Line Revision (read aloud before the exam)
  1. Electric current is the net rate of flow of charge through a cross-section, I = dQ/dt.
  2. Ohm's law states V = IR for metallic conductors at constant temperature.
  3. Resistance depends on material, length, and area: R = ρl/A.
  4. Resistivity is an intrinsic property; conductivity σ = 1/ρ.
  5. Drift velocity vd = (eEτ)/m is the average velocity of electrons under an electric field.
  6. Current density j = n e vd and j = σ E.
  7. Mobility μ = |vd|/E = eτ/m.
  8. Relaxation time τ is the average time between electron collisions.
  9. Temperature coefficient of resistivity α is positive for metals, negative for semiconductors.
  10. Power dissipated in a resistor is P = VI = I²R = V²/R.
  11. Emf ε is the open-circuit terminal voltage of a cell.
  12. Terminal voltage V = ε - Ir, where r is internal resistance.
  13. For series cells: εeq = ε1 + ε2, req = r1 + r2.
  14. For parallel cells: 1/req = 1/r1 + 1/r2, εeq/req = ε1/r1 + ε2/r2.
  15. Kirchhoff's junction rule: sum of currents entering = sum of currents leaving.
  16. Kirchhoff's loop rule: algebraic sum of potential changes in a closed loop is zero.
  17. In a conductor, electrons drift opposite to the electric field direction.
  18. Nichrome has a very low temperature coefficient, used in standard resistors.
  19. The SI unit of current is ampere (A).
  20. The SI unit of resistance is ohm (Ω).

MCQs — 10 Questions with Answers

Q1. Electric current is defined as I = ΔQ/Δt. What does ΔQ represent in this expression?

  • A. Total charge in the conductor
  • B. Net charge flowing across a cross-section in time interval Δt ✓
  • C. Magnitude of charge on a single electron
  • D. Charge density in the conductor

Answer: B — Current is the net charge (forward minus backward) crossing a cross-section per unit time, as stated in the definition given in the study material.

Q2. A conductor of length 50 cm and cross-sectional area 2 cm² has resistivity ρ = 1.7 × 10⁻⁸ Ω·m. Calculate its resistance.

  • A. 4.25 × 10⁻⁶ Ω
  • B. 4.25 × 10⁻⁴ Ω ✓
  • C. 8.5 × 10⁻⁴ Ω
  • D. 1.7 × 10⁻⁶ Ω

Answer: B — Using R = ρl/A: R = (1.7 × 10⁻⁸ × 0.50) / (2 × 10⁻⁴) = 8.5 × 10⁻⁹ / 2 × 10⁻⁴ = 4.25 × 10⁻⁵ Ω. (Note: Convert cm to m and cm² to m²; 2 cm² = 2 × 10⁻⁴ m².)

Q3. Why is there no net electric current in a conductor when no external electric field is applied?

  • A. Electrons are not moving inside the conductor
  • B. The random thermal motion of electrons results in equal flow in all directions, so net charge flow is zero ✓
  • C. Electrons are bound to nuclei and cannot move
  • D. Resistance is infinite at room temperature

Answer: B — Electrons undergo random collisions and thermal motion; equal numbers move in any direction versus the opposite direction, yielding zero net current without an applied field.

Q4. If the length of a uniform conductor is doubled while keeping its material and cross-sectional area constant, what happens to its resistance?

  • A. Resistance becomes half
  • B. Resistance doubles ✓
  • C. Resistance remains the same
  • D. Resistance becomes one-fourth

Answer: B — Since R = ρl/A and ρ and A are constant, resistance is directly proportional to length; doubling l doubles R, as shown in equation (3.4) of the study material.

Q5. Assertion (A): The drift velocity of electrons in a conductor is of the order of mm/s. Reason (R): The random thermal velocity of electrons is much larger than drift velocity.

  • A. Both A and R are true, and R is the correct explanation of A ✓
  • B. Both A and R are true, but R is not the correct explanation of A
  • C. A is true but R is false
  • D. Both A and R are false

Answer: A — Drift velocity is indeed very small (~mm/s) because electrons undergo frequent collisions, and R correctly explains why: thermal speeds are ~10⁵ m/s, so drift is a small net effect superimposed on rapid random motion.

Q6. Which of the following statements is NOT correct regarding Ohm's law and resistance?

  • A. Ohm's law V = IR applies to all conductors under all conditions ✓
  • B. Resistance R = ρl/A depends on material resistivity, length, and cross-sectional area
  • C. For a given material and geometry, increasing the length increases resistance
  • D. For a given material and length, increasing cross-sectional area decreases resistance

Answer: A — Ohm's law applies only to ohmic materials (where R is constant); non-ohmic materials like diodes and thermistors do not obey V = IR universally.

Q7. A cylindrical conductor has cross-sectional area A and length l. Another conductor is made by combining four identical conductors in series (end-to-end, same alignment). What is the resistance of the new combination?

  • A. R (where R is resistance of one conductor)
  • B. 2R
  • C. 4R ✓
  • D. R/4

Answer: C — Series combination: total length = 4l, area remains A. Since R ∝ l, the total resistance = 4 × (ρl/A) = 4R.

Q8. In a conductor with applied electric field E, electrons drift with velocity vd. Which of the following is true?

  • A. Drift velocity is independent of the applied electric field strength
  • B. Drift velocity is proportional to the applied electric field and inversely proportional to collision frequency ✓
  • C. Drift velocity equals the random thermal velocity of electrons
  • D. Drift velocity decreases when temperature increases because resistivity decreases

Answer: B — Drift velocity vd ∝ E-field (stronger field causes faster drift) and vd ∝ 1/(collision frequency) (more collisions reduce net drift); thermal speed is much larger and independent of E.

Q9. A copper wire at 0°C has resistance R₀ = 10 Ω. If its resistivity increases by 4% when heated to 50°C, what is its new resistance at 50°C?

  • A. 10.0 Ω
  • B. 10.4 Ω ✓
  • C. 10.2 Ω
  • D. 9.6 Ω

Answer: B — Since R = ρl/A and l and A remain constant, R is proportional to ρ. If ρ increases by 4%, then R increases by 4%: R = 10 × 1.04 = 10.4 Ω.

Q10. A battery maintains a steady electric field inside a conductor by continuously replenishing charge at its ends. Why is this necessary for steady current?

  • A. Without replenishment, electrons will leave the conductor completely
  • B. Without replenishment, the electric field would be neutralised by electron drift, and current would cease ✓
  • C. Replenishment is needed to accelerate electrons to higher speeds
  • D. Replenishment ensures that resistivity decreases over time

Answer: B — As shown in the study material, without charge replenishment (as in the initial dielectric-disc example), electrons neutralise the charges and the field vanishes, stopping the current; a battery continuously replenishes to maintain steady field and steady current.

Flashcards

Define electric current in terms of charge flow

Current I = ΔQ/Δt is the net charge flowing across a cross-section per unit time, in the limit of infinitesimal time interval.

What is the SI unit of current and how is it defined?

The SI unit is ampere (A), defined through the magnetic effects of currents (studied in the next chapter).

Why is there no net current in a conductor at thermal equilibrium with no applied field?

Electrons undergo random thermal motion and collide with ions; equal numbers move in all directions, so there is no preferential direction and no net charge flow.

State Ohm's law and define resistance

Ohm's law: V = IR, where V is potential difference, I is current, and R is resistance (the constant of proportionality between V and I).

How does the resistance of a conductor depend on its length and cross-sectional area?

Resistance is proportional to length (R ∝ l) and inversely proportional to cross-sectional area (R ∝ 1/A), combined as R = ρl/A.

What is drift velocity and what is its typical magnitude?

Drift velocity is the average velocity of free electrons in the direction of applied electric field; it is very small (order of mm/s) compared to random thermal speeds.

Define resistivity and state its unit

Resistivity ρ is the intrinsic resistance of a material per unit length and unit cross-sectional area; its SI unit is ohm-metre (Ω·m).

How does resistivity vary with temperature for metals and why?

Resistivity of metals increases with temperature because increased thermal motion raises collision frequency between electrons and ions, reducing drift velocity.

Distinguish between conventional current direction and electron flow direction

Conventional current is defined as the flow of positive charge and thus flows from positive to negative terminal, opposite to the actual motion of negatively charged electrons.

What role does a battery or cell play in maintaining steady current?

A battery maintains a steady electric field inside the conductor by continuously replenishing charge at the ends, ensuring a continuous current rather than transient current.

Important Board Questions

Define electric current and state its SI unit. Explain why no net current flows in a conductor at thermal equilibrium with no applied electric field. [2 marks]

Define I = ΔQ/Δt and state unit is ampere. For no net current: explain that random thermal motion gives equal electron flow in all directions, so net charge crossing any section is zero.

A uniform conductor of length l and cross-sectional area A is made of material with resistivity ρ. Derive the relation R = ρl/A by considering two identical slabs placed in series. Hence, explain how resistance depends on the geometry of the conductor. [5 marks]

Combine two identical slabs (length l each, area A) in series: total length 2l, same V across each slab, same I through both. Use Ohm's law V = IR for each slab and combination to show Rc = 2R, proving R ∝ l. Then consider parallel arrangement to show R ∝ 1/A, deriving R = ρl/A.

Explain the mechanism of current flow in a solid conductor. Describe the roles of thermal motion of electrons, collision frequency, applied electric field, and drift velocity in establishing steady current. Why is the resistivity of metals temperature-dependent? Show how a battery or cell maintains steady current in a circuit. [6 marks]

Explain: (1) Without field, random thermal motion → no net current. (2) Applied E-field gives preferential drift direction superimposed on thermal motion. (3) Drift velocity vd ∝ E and vd ∝ 1/(collision frequency). (4) Temperature ↑ → collision frequency ↑ → ρ ↑ (explain microscopically). (5) Battery maintains steady E-field inside conductor by continuously supplying charge, preventing neutralisation and keeping current steady (reference the dielectric-disc example from study material).

Assertion-Reason Questions for Current Electricity

Q1. Assertion (A):

The resistance of a cylindrical conductor is directly proportional to its length.

Reason (R):

As length increases, the number of collisions electrons undergo with fixed ions increases, restricting their drift velocity.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both the assertion and reason are true, and the reason correctly explains why resistance increases with length. The increased path length provides more opportunities for electron-ion collisions, which is the physical basis for R ∝ l shown in Eq. 3.5.

Q2. Assertion (A):

In steady-state conduction, the electric current at every cross-section of a conductor must be the same.

Reason (R):

Because charge cannot accumulate at any point inside the conductor in steady state, it follows from conservation of charge.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both statements are true, and the reason provides the fundamental principle (conservation of charge) that explains the assertion. This is the continuity equation for steady currents, ensuring charge entering any segment equals charge leaving.

Q3. Assertion (A):

Thermal motion of electrons in a conductor occurs even in the absence of an applied electric field.

Reason (R):

Because at room temperature, electrons possess kinetic energy due to thermal energy, causing them to move randomly inside the conductor.

Answer: B — Both A and R are true, but R is NOT the correct explanation of A — Both the assertion and reason are true. Electrons do exhibit random thermal motion (Section 3.3), and this is indeed due to thermal energy. However, the reason does not fully explain why there is no net current despite this motion—the key point is that motion is random with no preferred direction. The reason is incomplete as an explanation.

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Case-Based Questions (CBQ) for Current Electricity

Case Study:

A power distribution company in Delhi supplies electricity to residential areas through copper cables buried underground. The main feeder cable has a length of 2 km, a cross-sectional area of 50 mm², and resistivity of copper is 1.7 × 10⁻⁸ Ω·m. During peak demand in summer, a current of 100 A flows through this cable. The cable is exposed to underground temperature variations, which affect its resistance. According to specifications, copper's resistance increases by 0.4% for every 1°C rise in temperature above 20°C.

Q1. What is the resistance of the main feeder cable at 20°C?

  • A. 0.68 Ω ✓
  • B. 6.8 Ω
  • C. 68 Ω
  • D. 0.068 Ω

Answer: A

Q2. If the underground temperature rises to 40°C (ΔT = 20°C), what is the new resistance of the cable?

  • A. 0.68 Ω
  • B. 0.73 Ω
  • C. 0.74 Ω ✓
  • D. 1.36 Ω

Answer: C

Q3. What is the potential difference (voltage drop) across the cable when current is 100 A at 20°C?

  • A. 6.8 V ✓
  • B. 68 V
  • C. 680 V
  • D. 0.68 V

Answer: A

Q4. How much additional power is dissipated as heat in the cable due to the temperature rise from 20°C to 40°C?

  • A. 800 W
  • B. 680 W
  • C. 600 W ✓
  • D. 600 W increase from baseline

Answer: C

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Previous Year Questions (PYQ) for Current Electricity

Real CBSE board exam questions from past papers — free to attempt.

CBSE 2026 · Set 55/1/1 · 1 mark

Two heaters rated as (P₁, V) and (P₂, V) are connected in series across a dc source of V/2 volt. The power consumed by the combination will be

  • (P₁ + P₂)
  • (P₁ + P₂)/2
  • P₁P₂/(2(P₁ + P₂))
  • P₁P₂/(4(P₁ + P₂))

CBSE 2026 · Set 55/1/1 · 2 marks

What is the order of magnitude of drift velocity of electrons in a conductor ? Deduce the relation between the current flowing through a conductor and drift velocity of electrons in it.

CBSE 2026 · Set 55/1/1 · 4 marks

A galvanometer is used to detect or/and measure small currents in an electrical circuit. It essentially works on the fact that a current-carrying coil experiences a deflecting torque when placed in a magnetic field. This deflection in the coil can be measured and it is related to the current flowing in the coil, the number of turns in the coil, area of the coil and the magnetic field. A hair spring attached to the coil provides a counter torque and helps in measuring the deflection. A galvanometer can be converted to an ammeter or a voltmeter of desired range by using suitable resistances.

The torque on the coil remains constant irrespective of the coil's orientation during rotation due to

  • use of soft iron core which increases the magnetic field.
  • radial magnetic field
  • hair spring which provides the counter torque
  • eddy current in the iron core which causes damping.

CBSE 2026 · Set 55/1/2 · 1 mark

A copper wire is stretched to increase its length by 1%. Then the change in its resistance is close to

  • 1%
  • 4%
  • −4%
  • 2%

CBSE 2026 · Set 55/1/2 · 2 marks

What is the order of magnitude of drift velocity of electrons in a conductor? Deduce the relation between the current flowing through a conductor and drift velocity of electrons in it.

CBSE 2026 · Set 55/1/2 · 3 marks

Figure shows a narrow beam of electrons entering with a velocity of 3 × 107 m/s, symmetrically through the space between two parallel horizontal plates P1 P1' and P2 P2' kept 2 cm apart. If each plate is 3 cm long, calculate the potential difference V applied between the plates so that the beam just strikes the end P2'.

CBSE 2026 · Set 55/1/3 · 1 mark

A current of 1.5 A is maintained in a copper wire of length 1 m with area of cross-section 1.7 × 10⁻⁷ m². The magnitude of electric field in the wire is [ρ_Cu = 1.7 × 10⁻⁸ Ω m)

  • 0.15 V/m
  • 0.30 V/m
  • 1.5 V/m
  • 3.0 V/m

CBSE 2026 · Set 55/2/1 · 1 mark

A galvanometer of resistance 27 Ω is converted into an ammeter of range (0 – 10 mA) using a resistance of 3 Ω. The galvanometer will show full scale deflection for a current of about

  • 10 mA
  • 100 mA
  • 1 mA
  • 3 mA

CBSE 2026 · Set 55/2/1 · 1 mark

Assertion (A): Two electric heaters of power P₁ and P₂ (> P₁) are joined in series across a dc source of voltage V. The power consumed by the combination will be less than that consumed by P₁ when connected across the same source. Reason (R): The power consumed by a electric device when connected to a dc source of voltage V is proportional to its resistance.

  • Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
  • Assertion (A) is true, but Reason (R) is false.
  • Assertion (A) is false and Reason (R) is also false.

CBSE 2026 · Set 55/2/1 · 2 marks

A heating element using nichrome is connected to a 220 V supply. Initially it draws a current of 2.9 A. After some time, the current attains a steady value of 2.5 A. Find the steady temperature of the heating element if the room temperature is 27 °C. The temperature coefficient of resistance of nichrome is 1.7 × 10⁻⁴ °C⁻¹.

CBSE 2026 · Set 55/2/1 · 3 marks

(a) Explain the statement: "Current is a scalar although we represent current with an arrow". (b) Use Kirchhoff's rules to find the current through 3 Ω resistor in the circuit shown in the figure:

CBSE 2026 · Set 55/2/1 · 5 marks

(a) An electric field E⃗ is established across the ends of a cylindrical conductor of length L and area of cross-section A. Discuss how electrons attain an average velocity, independent of time. Hence, obtain a relation between current in the conductor and this 'average velocity' of electrons. (b) (i) This 'average velocity' is found be few mm s⁻¹ for currents in range of a few amperes. How then is current established almost the instant a circuit is closed? (ii) Two copper wires having their radii in the ratio of 3 : 2 are connected in series across a battery. Find the ratio of the drift velocities of the electrons in the wires.

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Class 12 Physics Formula Sheet

Every formula from all 14 chapters on one page, checked against the NCERT textbook and the CBSE 2026-27 syllabus. Free PDF download.

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Class 12 Physics Previous Year Questions, Chapter-wise

All 962 CBSE board questions from 2022–2026, sorted by chapter and question type. Free PDF download.

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Class 12 Physics Derivations

All 68 derivations, chapter-wise, step by step with diagrams and marked with the CBSE board years (2022–2026) each was asked in. Free PDF download.

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