NCERT Solutions for Class 12 Physics Chapter 3 Current Electricity
NCERT Solutions for Class 12 Physics Chapter 3 Current Electricity provides detailed revision notes, formulas, derivations, and step-by-step textbook solutions covering electric current, Ohm's law, drift velocity, resistivity, cells, Kirchhoff's laws, and Wheatstone bridge.
Overview of Topics & Subtopics (Click to Jump)
1. Electric Current, Drift Velocity & Ohm's Law
Short Note:
• Electric Current (I): The rate of flow of charge across any cross-section of a conductor: I = dQ / dt. SI unit is Ampere (A).
• Drift Velocity (v_d): Average velocity with which free electrons drift towards the positive terminal under an applied electric field: v_d = (e E / m) × τ (where τ is relaxation time).
• Relation between Current & Drift Velocity: I = n e A v_d, where n is charge carrier density and A is cross-sectional area.
• Current Density (J): Current per unit area: J = I / A = n e v_d. Vector form of Ohm's Law: J = σ E (where σ is electrical conductivity).
• Ohm's Law: Current flowing through a conductor is directly proportional to potential difference applied across its ends provided physical conditions (temperature, pressure) remain constant: V = IR.
• Resistance (R): Opposition offered to the flow of current: R = ρ L / A, where ρ is electrical resistivity.
2. Electrical Energy, Power & Temperature Dependence of Resistivity
Short Note:
• Electrical Power (P): Rate at which electrical energy is consumed or dissipated in a circuit: P = VI = I²R = V² / R. SI unit is Watt (W).
• Electrical Energy (W): Total work done by charge carriers: W = P × t = V I t = I² R t. SI unit is Joule (J); commercial unit is kWh (1 kWh = 3.6 × 10⁶ J).
• Temperature Dependence of Resistivity:
- Metallic Conductors: Resistivity increases with temperature: ρ_T = ρ₀ [1 + α(T - T₀)], where α is temperature coefficient of resistivity (+ve for metals).
- Semiconductors & Insulators: Resistivity decreases exponentially as temperature increases (α is negative).
- Alloys (e.g., Manganin, Constantan): Resistivity is very high and almost independent of temperature (very small α).
3. EMF, Internal Resistance & Combination of Cells
Short Note:
• Electromotive Force (EMF, E): Maximum potential difference between cell terminals when no current is drawn from it (open circuit).
• Terminal Potential Difference (V): Potential difference across terminals when current is drawn (closed circuit): V = E - I r (during discharge) and V = E + I r (during charging).
• Internal Resistance (r): Opposition offered by electrolyte and electrodes to internal current flow: r = R (E / V - 1).
• Combination of Cells:
- Series Combination: E_eq = E₁ + E₂, r_eq = r₁ + r₂.
- Parallel Combination: E_eq / r_eq = E₁ / r₁ + E₂ / r₂ and 1 / r_eq = 1 / r₁ + 1 / r₂.
4. Kirchhoff's Laws & Wheatstone Bridge
Short Note:
• Kirchhoff's First Law / Junction Rule (KCL): Algebraic sum of currents meeting at any junction in a closed circuit is zero (∑ I = 0). Based on Conservation of Charge.
• Kirchhoff's Second Law / Loop Rule (KVL): Algebraic sum of potential changes around any closed loop is zero (∑ ΔV = 0 or ∑ E = ∑ IR). Based on Conservation of Energy.
• Wheatstone Bridge: An arrangement of four resistors (P, Q, R, S) used to determine an unknown resistance.
- Balanced Condition: When no current flows through galvanometer (I_g = 0): P / Q = R / S.
Intext & Conceptual Questions
• Conductors: Resistivity is given by ρ = m / (n e² τ). In metallic conductors, the free electron density (n) is already very high and stays nearly constant with temperature. As temperature increases, thermal vibrations of lattice ions increase, causing more frequent collisions. This decreases the relaxation time (τ), thereby increasing resistance.
• Semiconductors: As temperature increases, more covalent bonds break, generating a significant number of additional charge carriers (electron-hole pairs). The exponential increase in charge carrier density (n) dominates over the decrease in relaxation time (τ), resulting in a net decrease in resistance.
| Feature | Electromotive Force (EMF) | Terminal Potential Difference (V) |
|---|---|---|
| Circuit State | Measured in an open circuit (when no current flows). | Measured in a closed circuit (when current flows). |
| Internal Resistance Effect | Independent of internal resistance and external load. | Depends on internal resistance and external load resistance. |
| Magnitude Relation | Always greater than terminal voltage during cell discharge (E > V). | Less than EMF during discharge (V = E - Ir). |
| Source vs Effect | It is the cause/source of potential difference. | It is the effect observed across circuit components. |
Textbook Chapter End Exercise Questions
Given:
• EMF of battery (E) = 8.0 V
• Internal resistance of battery (r) = 0.5 Ω
• DC supply voltage (V_supply) = 120 V
• Series resistor (R) = 15.5 Ω
Step 1: Net Effective Voltage in circuit during charging
V_net = V_supply - E = 120 V - 8.0 V = 112 V
Step 2: Total resistance of circuit
R_total = R + r = 15.5 + 0.5 = 16.0 Ω
Step 3: Charging Current (I)
I = V_net / R_total = 112 / 16 = 7.0 A
Step 4: Terminal Voltage during charging
V = E + I r = 8.0 + (7.0 × 0.5) = 8.0 + 3.5 = 11.5 V
Purpose of Series Resistor: The series resistor limits the heavy charging current. Without it, high current would flow, damaging the battery and supply unit due to excessive heating.
| Feature | Ohmic Conductors | Non-Ohmic Conductors |
|---|---|---|
| Ohm's Law Validity | Obey Ohm's law (V ∝ I) at all voltages. | Do not obey Ohm's law; V/I ratio is non-constant. |
| V-I Graph Characteristic | Linear straight line passing through origin. | Non-linear curve or non-symmetric behavior. |
| Resistance Value | Constant resistance independent of current. | Dynamic resistance depends on current/voltage. |
| Examples | Copper wire, Silver wire, Metallic resistors. | Semiconductor diodes, Transistors, Vacuum tubes, Electrolytes. |
Read More & Chapter Resources
These short notes are designed for quick revision. Read the main points once, then use the related material below to practise the same chapter. Revising a concept and checking it with questions can make your preparation more focused.