Current Electricity — Physics Class 12 Notes (CBSE & HBSE)
Free NCERT Physics notes for Current Electricity (Class 12) on Siksha Sarovar, aligned to CBSE and Haryana Board (HBSE). This chapter is broken into 3 topics with clear explanations, formulas, solved examples and board-pattern practice — free to read, no sign-up required.
Board exam focus — Current Electricity (CBSE & HBSE)
CBSE focuses on drift velocity derivation, Kirchhoff's laws with complex circuit problems, and potentiometer applications. HBSE emphasizes Ohm's law, resistivity, temperature dependence, and Wheatstone bridge principle with direct numericals.
Ohm's Law, Resistance and Drift Velocity
Electric Current
Electric current is the rate of flow of charge through a cross-section:
I = dQ/dt = Q/t
Unit: Ampere (A). Direction of conventional current = direction of positive charge flow (opposite to electron flow).
Drift Velocity
Free electrons in a conductor have random thermal motion (v_thermal ~ 10⁵ m/s). In the absence of field, net flow = 0. When electric field is applied, electrons acquire a net drift in the direction opposite to E:
v_d = eEτ/m
where τ = relaxation time (mean time between collisions), e = electron charge, m = electron mass.
Current in Terms of Drift Velocity
For a conductor of cross-sectional area A with n free electrons per unit volume:
I = nAev_d
where n = number density of electrons (m⁻³)
Ohm's Law
V = IR
- V: potential difference (Volt)
- I: current (Ampere)
- R: resistance (Ohm, Ω)
A material obeys Ohm's law if R is constant (independent of V and I). Non-ohmic materials (diodes, transistors) have V–I characteristics that are non-linear.
Resistance and Resistivity
R = ρL/A
where:
- ρ (rho) = resistivity (Ω·m) — intrinsic property of material
- L = length of conductor
- A = cross-sectional area
| Material | Resistivity ρ (Ω·m) | Type |
|---|---|---|
| Silver | 1.6×10⁻⁸ | Conductor |
| Copper | 1.7×10⁻⁸ | Conductor |
| Nichrome | 1.0×10⁻⁶ | Alloy |
| Germanium | ~10⁻² | Semiconductor |
| Silicon | 10²–10³ | Semiconductor |
| Glass | 10¹⁰–10¹⁴ | Insulator |
Temperature Dependence of Resistance
For metals, resistance increases with temperature:
R_T = R₀(1 + αΔT)
where α = temperature coefficient of resistance (°C⁻¹ or K⁻¹)
- Metals: α > 0 (resistance increases with T)
- Semiconductors/electrolytes: α < 0 (resistance decreases with T)
- Alloys (Nichrome, Manganin): α ≈ 0 (resistance nearly constant)
Conductance and Conductivity
- Conductance G = 1/R (Unit: Siemens, S)
- Conductivity σ = 1/ρ (Unit: S/m or Ω⁻¹·m⁻¹)
V-I Characteristics
- Ohmic conductor: Straight line through origin (R constant)
- Tungsten filament lamp: Curve (R increases with T)
- p-n junction diode: Non-linear (different forward/reverse)
- Electrolytes: Between ohmic and non-ohmic
EMF and Internal Resistance
For a battery with EMF ε and internal resistance r:
Terminal voltage: V = ε − Ir
- On charging: V = ε + Ir (terminal voltage > EMF)
- On discharging: V = ε − Ir (terminal voltage < EMF)
Power delivered to external circuit: P = I(ε − Ir) = I·V
Diagram Indicator: [V-I graph showing straight line for ohmic conductor and curve for non-ohmic; also drift of electrons in conductor with field E applied, showing small net drift v_d opposite to E.]
Kirchhoff's Laws and Circuits
Kirchhoff's Current Law (KCL) — Junction Rule
The algebraic sum of all currents at any junction (node) in a circuit is zero:
ΣI = 0 at junction (currents in = currents out)
Based on conservation of charge.
Kirchhoff's Voltage Law (KVL) — Loop Rule
The algebraic sum of all EMFs and potential drops around any closed loop is zero:
Σε = ΣIR (around any closed loop)
Based on conservation of energy.
Sign Convention for KVL
- Traversing a resistor in direction of assumed current: voltage drop = −IR
- Traversing a resistor against current: voltage rise = +IR
- Traversing a battery from − to +: voltage rise = +ε
- Traversing a battery from + to −: voltage drop = −ε
Series Combination of Resistors
Resistors in series carry the same current: R_eq = R₁ + R₂ + R₃ + ... V = V₁ + V₂ + V₃
Parallel Combination of Resistors
Resistors in parallel have the same voltage: 1/R_eq = 1/R₁ + 1/R₂ + 1/R₃ + ... I = I₁ + I₂ + I₃
For two resistors: R_eq = R₁R₂/(R₁ + R₂)
Comparison: Series vs Parallel
| Property | Series | Parallel |
|---|---|---|
| Current | Same | Different |
| Voltage | Different | Same |
| R_equivalent | R₁+R₂+... | Less than smallest R |
| Use | Voltage divider | Current divider |
Cells in Series and Parallel
n cells in series: ε_eq = nε, r_eq = nr, I = nε/(R+nr) n cells in parallel: ε_eq = ε, r_eq = r/n, I = ε/(R+r/n) Mixed grouping (m rows × n cells): I = mnε/(mR+nr)
Power in Electrical Circuits
P = VI = I²R = V²/R (Watt)
Energy consumed: W = Pt = VIt = I²Rt
Heating effect (Joule's law): H = I²Rt
Maximum Power Transfer Theorem
Maximum power is delivered to external resistance R when R = r (internal resistance):
P_max = ε²/(4r)
Diagram Indicator: [Circuit diagram with two loops showing KVL analysis: currents I₁, I₂, I₃ at junction demonstrating KCL; loop equations demonstrating KVL with marked EMFs and resistors.]
Wheatstone Bridge, Meter Bridge and Potentiometer
Wheatstone Bridge
A Wheatstone bridge is a circuit used to measure an unknown resistance precisely.
Four resistors P, Q, R, S arranged in a diamond:
Balanced condition: P/Q = R/S → I_G = 0 (no current through galvanometer)
Used to find unknown S = QR/P
Meter Bridge
A practical form of Wheatstone bridge using a uniform wire of length 100 cm.
Working principle: At balance: P/Q = R/S → R_wire(l)/(R_wire(100−l)) = R/S
Since wire has uniform resistance per unit length: R/S = l/(100−l)
Unknown S = R(100−l)/l
Sensitivity increases when balance point is near the middle (l ≈ 50 cm).
Potentiometer
A potentiometer is a long uniform resistance wire used to measure EMF or compare EMFs precisely.
Principle: When a cell drives current through a uniform wire, the potential drop across length l is:
V = φl
where φ = potential gradient (V/m) = V_total/L
Applications of Potentiometer
1. Comparing EMFs: ε₁/ε₂ = l₁/l₂
(Find balance lengths l₁ and l₂ for each cell separately)
2. Measuring Internal Resistance: In open circuit: balance at length l₁ With external resistance R: balance at length l₂
r = R(l₁ − l₂)/l₂
3. Measuring small EMFs (thermocouples) accurately
Potentiometer vs Voltmeter
| Feature | Potentiometer | Voltmeter |
|---|---|---|
| Current drawn | Zero at balance | Small but finite |
| Accuracy | Very high (null method) | Limited by resistance |
| Measures | EMF accurately | Terminal voltage |
| Internal resistance | Does not affect reading | Affects reading |
Sensitivity of Potentiometer
- Higher sensitivity = longer wire or lower potential gradient φ
- Sensitivity can be increased by using a rheostat to reduce driving current
- Sensitivity ∝ 1/φ = L/V
Galvanometer as Measuring Instrument
- Current sensitivity: deflection per unit current (div/A or div/μA)
- Voltage sensitivity: deflection per unit voltage
- Conversion to Ammeter: connect low resistance shunt in parallel: I_s = I_g(G)/(S) → S = I_g·G/(I − I_g)
- Conversion to Voltmeter: connect high resistance series resistor: R = V/I_g − G
Diagram Indicator: [Wheatstone bridge diamond circuit with P,Q,R,S and galvanometer G; also potentiometer circuit showing long wire AB, driving cell, and test cell with jockey showing balance point at length l.]
Frequently asked questions
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Do these notes follow CBSE and HBSE?
Yes. The Current Electricity notes are NCERT-aligned and include guidance for both CBSE and Haryana Board (HBSE), with important questions and MCQs for revision.
What does the Current Electricity chapter cover?
Concept explanations, key formulas and definitions, fully solved examples and board-pattern practice questions for Current Electricity.