Class 12 Physics · Chapter 3 NotesCurrent Electricity
Revise Class 12 Physics Current Electricity with clear notes on current, Ohm's law, resistivity, drift velocity, cells, Kirchhoff's rules and Wheatstone bridge.
Current Electricity is the study of charges in steady motion. In earlier chapters charges were treated at rest; here we learn how a steady electric field inside a conductor makes free electrons drift and produce a current. The chapter begins with the definition of current and current density, then explains how a simple model of electron drift and collisions reproduces Ohm's law and gives resistivity in terms of electron number density and relaxation time. It goes on to describe how resistivity changes with temperature, how electrical energy is dissipated as heat, and how a cell maintains a steady current through its emf and internal resistance. Finally, Kirchhoff's junction and loop rules are introduced for analysing circuits that cannot be reduced to simple series and parallel combinations, with the Wheatstone bridge as an application.
What you'll learn
1Define electric current and current density, and relate current to drift velocity.
2State Ohm's law and derive the dependence of resistance on length, area and resistivity.
3Explain drift velocity, relaxation time and mobility using the free-electron model.
4Describe how resistivity varies with temperature for metals, alloys and semiconductors.
5Calculate electrical power dissipated in a resistor and explain power loss in transmission cables.
6Define emf and internal resistance, and find the terminal voltage of a cell.
7Apply Kirchhoff's junction and loop rules to solve multi-loop circuits.
8Use the balance condition of a Wheatstone bridge to determine an unknown resistance.
Chapter at a glance
01Electric Current and Drift Velocity
02Ohm's Law and Resistivity
03EMF, Internal Resistance, and Kirchhoff's Laws
04Series and Parallel Circuits
Detailed chapter notes
01
Electric Current and Current Density
Electric current is the rate of flow of charge across a cross-section of a conductor. If a net charge ΔQ crosses an area in time Δt, the current is I = ΔQ/Δt, and in the limit Δt tending to zero it becomes the instantaneous current. The SI unit is the ampere. Current is a scalar even though we draw arrows to show its direction. Current density j is the current per unit area taken normal to the flow, j = I/A, measured in A/m². For a conductor of cross-section A carrying current I, the current density is uniform if the current is steady. In solid conductors the current is carried by free electrons moving opposite to the applied electric field.
I = ΔQ/Δt (instantaneous current in the limit Δt → 0)
SI unit of currentampere (A)
Current density j = I/A, unit A/m²
Current is a scalar quantity; arrows only show direction of flow
02
Ohm's Law, Resistance and Resistivity
Ohm's law states that the current through a conductor is proportional to the potential difference across its ends, V = IR, where R is the resistance. The unit of resistance is the ohm (Ω), with 1 Ω = 1 V A⁻¹. Resistance depends on the dimensions of the conductor: doubling the length doubles the resistance, while doubling the cross-sectional area halves it. Combining these, R = ρl/A, where ρ is the resistivity of the material, a property that does not depend on the shape or size of the conductor. In vector form Ohm's law is written j = σE, where σ = 1/ρ is the conductivity. Current density j is parallel to the electric field E.
V = IR
R = ρl/A
j = σE, where σ = 1/ρ is conductivity
Unit of resistivityohm metre (Ω m)
03
Drift of Electrons and Origin of Resistivity
In a metal, free electrons move randomly and collide with fixed positive ions. Without an electric field the average velocity of electrons is zero. When a field E is applied, each electron accelerates between collisions and the average velocity becomes the drift velocity vd = (eE/m)τ, where τ is the average time between collisions called the relaxation time. The current density is j = ne²τE/m, which matches Ohm's law if conductivity σ = ne²τ/m and resistivity ρ = m/(ne²τ). Mobility μ is the magnitude of drift velocity per unit electric field, μ = vd/E = eτ/m, measured in m² V⁻¹ s⁻¹. Drift speeds are very small, but the electric field is established almost instantly throughout the circuit.
Drift velocity vd = (eE/m)τ
Current density j = ne²τE/m
Resistivity ρ = m/(ne²τ)
Mobility μ = vd/E = eτ/m
04
Temperature Dependence of Resistivity
Over a limited temperature range, the resistivity of a metallic conductor increases approximately linearly with temperature: ρT = ρ0[1 + α(T − T0)], where α is the temperature coefficient of resistivity. For metals α is positive because the number density n of free electrons stays nearly constant while the relaxation time τ decreases as temperature rises. Alloys like nichrome, manganin and constantan show a very weak dependence on temperature, so they are used for standard resistors. In semiconductors and insulators, n increases rapidly with temperature and this increase outweighs the decrease in τ, so resistivity decreases as temperature rises.
ρT = ρ0[1 + α(T − T0)]
Metalsα positive, resistivity increases with temperature
Alloysvery small α, used in standard resistors
Semiconductorsresistivity decreases with temperature
05
Electrical Energy and Power
When a charge ΔQ moves through a potential difference V, its potential energy changes by −ΔQV. In a conductor the collisions prevent the kinetic energy from increasing, so this energy appears as heat. The power dissipated in a resistor is P = IV, which using Ohm's law becomes P = I²R = V²/R. This is the ohmic loss that heats the filament of a bulb or the element of a heater. In power transmission, the wasted power in the cables is Pc = P²Rc/V², so transmitting at very high voltage greatly reduces the loss. Transformers then lower the voltage to a safe value for domestic use.
P = IV
P = I²R = V²/R
Power wasted in cablesPc = P²Rc/V²
High-voltage transmission reduces power loss
06
Cells, EMF and Internal Resistance
A cell maintains a steady current by converting chemical energy into electrical energy. Its electromotive force (emf) ε is the potential difference between its terminals when no current is drawn, that is, in an open circuit. In reality the electrolyte offers an internal resistance r, so when a current I flows through an external resistance R, the terminal voltage is V = ε − Ir. The current in the circuit is I = ε/(R + r). The maximum current a cell can deliver is ε/r when R = 0, but cells are usually not operated at this value because it can damage them.
emf ε = terminal voltage in open circuit
Terminal voltage V = ε − Ir
Circuit current I = ε/(R + r)
Maximum current Imax = ε/r (for R = 0)
07
Combination of Cells
Cells can be connected in series or in parallel, just like resistors. In a series combination, the equivalent emf is the algebraic sum of the individual emfs and the equivalent internal resistance is the sum of the internal resistances: εeq = ε1 + ε2 and req = r1 + r2. If a cell is connected with opposite polarity, its emf enters with a negative sign. In a parallel combination, the reciprocals of the internal resistances add: 1/req = 1/r1 + 1/r2, and the equivalent emf is given by εeq/req = ε1/r1 + ε2/r2. These rules extend to any number of cells.
Seriesεeq = ε1 + ε2, req = r1 + r2
Parallel1/req = 1/r1 + 1/r2
Parallelεeq/req = ε1/r1 + ε2/r2
Reverse polarityemf enters with a negative sign
08
Kirchhoff's Rules and Wheatstone Bridge
Kirchhoff's rules are used for circuits that cannot be reduced to simple series and parallel combinations. The junction rule states that the sum of currents entering a junction equals the sum of currents leaving it, which follows from conservation of charge. The loop rule states that the algebraic sum of changes in potential around any closed loop is zero, which follows from conservation of energy. The Wheatstone bridge is a four-resistor network used to measure an unknown resistance. When the galvanometer shows no deflection, the bridge is balanced and the condition is R1/R2 = R3/R4, so R4 = R3R2/R1.
Junction rulesum of currents in = sum of currents out
Loop rulealgebraic sum of potential changes around a closed loop = 0
Wheatstone bridge balance conditionR1/R2 = R3/R4
Unknown resistanceR4 = R3R2/R1
Want the complete chapter resources?Topic notes, quizzes and flashcards for Current Electricity.
Electric current is defined as the rate of flow of electric charge. If a charge of 10 C flows through a conductor in 5 seconds, what is the current?
A0.5 A
B2 A
C5 A
D50 A
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Answer: (B) 2 A
Current I = Q/t = 10 C / 5 s = 2 A. This is a direct application of the definition of electric current.
Question 02
What does Ohm's Law state?
AV = IR, where V is voltage, I is current, and R is resistance
BP = VI, where P is power, V is voltage, and I is current
CR = ρL/A, where ρ is resistivity, L is length, and A is area
DI = Q/t, where I is current, Q is charge, and t is time
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Answer: (A) V = IR, where V is voltage, I is current, and R is resistance
Ohm's Law defines the linear relationship between voltage, current, and resistance. It states that the current flowing through a conductor is directly proportional to the voltage applied and inversely proportional to its resistance.
Question 03
The electromotive force (EMF) of a cell is defined as:
AThe potential difference across the terminals of the cell when current flows
BThe work done per unit charge by the non-electrostatic forces inside the cell
CThe voltage drop across the internal resistance
DThe rate of energy dissipation in the external circuit
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Answer: (B) The work done per unit charge by the non-electrostatic forces inside the cell
EMF is defined as the work done per unit positive charge by non-electrostatic (chemical) forces inside the cell, independent of current flow.
Question 04
In a series circuit with three resistors, how many paths are available for current to flow?
AOne path only
BTwo paths
CThree paths
DMultiple paths depending on resistance
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Answer: (A) One path only
In a series circuit, components are connected end-to-end, providing only one continuous path for current to flow through all resistors sequentially.
Question 05
What is drift velocity?
AThe velocity of free electrons in the absence of an electric field
BThe average velocity of charge carriers in response to an applied electric field
CThe maximum velocity attained by electrons in a conductor
DThe velocity of electrons at absolute zero temperature
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Answer: (B) The average velocity of charge carriers in response to an applied electric field
Drift velocity is the slow, directed motion of charge carriers (usually electrons) through a conductor when an electric field is applied, despite their random thermal motion.
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Q1. Define drift velocity. How is it related to the current density in a conductor?
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Model answer
Drift velocity is the average velocity acquired by free electrons in a conductor under the influence of an electric field. It is given by v_d = (eEτ)/m. The current density j is related to drift velocity by j = n e v_d, where n is the number density of electrons and e is the electron charge.
Sample question3 marks
Q2. State Ohm's law. How is it expressed in terms of current density and electric field?
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Model answer
Ohm's law states that the potential difference V across a conductor is directly proportional to the current I flowing through it, provided physical conditions remain constant, i.e., V ∝ I or V = IR. In terms of current density j and electric field E, it is expressed as E = ρ j or j = σ E, where ρ is resistivity and σ is conductivity.
Sample question3 marks
Q3. Define emf of a cell. How does the terminal voltage of a cell differ from its emf when it is supplying current?
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Model answer
The emf of a cell is the potential difference between its positive and negative terminals in an open circuit (when no current is drawn). When the cell supplies current, the terminal voltage V is less than the emf ε due to the drop across its internal resistance r, given by V = ε – Ir, where I is the current.
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Q4. Derive the expression for the equivalent resistance of two resistors connected in series.
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Model answer
When two resistors R1 and R2 are connected in series, the same current I flows through both. The total potential difference V across the combination is the sum of individual potential differences: V = V1 + V2 = IR1 + IR2 = I(R1 + R2). Thus, the equivalent resistance Rs = V/I = R1 + R2.
Sample question3 marks
Q5. Explain why the drift velocity of electrons is very small (of the order of mm/s) even though the electric field propagates at nearly the speed of light.
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Model answer
Drift velocity is small because electrons undergo frequent collisions with ions in the conductor. The average time between collisions (relaxation time) is very short, so the net acceleration is limited. In contrast, the electric field propagates as an electromagnetic wave at nearly the speed of light, establishing the field almost instantly throughout the circuit.
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Electric current is the net rate of flow of charge across a cross-section of a conductor. If a net charge ΔQ crosses an area in time Δt, the current is I = ΔQ/Δt. In the limit Δt tending to zero, this gives the instantaneous current. The SI unit of current is the ampere (A).
What is the difference between resistance and resistivity?
Resistance R is a property of a particular conductor and depends on its length and area, R = ρl/A. Resistivity ρ is a property of the material itself and does not depend on the dimensions of the conductor. The SI unit of resistance is ohm (Ω) and that of resistivity is ohm metre (Ω m).
Why does the resistivity of a metal increase with temperature?
In a metal, the number density n of free electrons is nearly independent of temperature. As temperature rises, electrons collide more frequently with the vibrating ions, so the relaxation time τ decreases. Since resistivity ρ = m/(ne²τ), a decrease in τ causes ρ to increase.
What is drift velocity and why is it so small?
Drift velocity is the average velocity acquired by free electrons in the direction opposite to the applied electric field. It is given by v_d = (eE/m)τ. It is small because electrons collide frequently with ions; each collision randomises their velocity, so the average drift is only a few mm per second.
How do you find the terminal voltage of a cell?
The terminal voltage is the potential difference across the external circuit when a current is drawn. It is given by V = ε − Ir, where ε is the emf of the cell, I is the current and r is the internal resistance. When no current flows, the terminal voltage equals the emf.
What is the balance condition of a Wheatstone bridge?
A Wheatstone bridge is balanced when the galvanometer shows zero deflection, meaning no current flows through it. The balance condition is R1/R2 = R3/R4, where R1, R2, R3 and R4 are the four resistances in the bridge. This allows an unknown resistance to be calculated from the other three.