Class 12 Physics Notes Chapter 3 (Current Electricity) – Examplar Problems (English) Book
Alright class, let's get straight into Chapter 3: Current Electricity. This is a fundamental chapter for your Class 12 Physics and crucial for various government exams that include Physics. We'll cover the core concepts, formulas, and principles you absolutely need to know. Pay close attention to the definitions, laws, and applications of the instruments.
Chapter 3: Current Electricity - Detailed Notes for Exam Preparation
1. Electric Current (I)
- Definition: The rate of flow of electric charge through any cross-section of a conductor.
- Formula: I = ΔQ / Δt (Average current) or I = dQ/dt (Instantaneous current)
- SI Unit: Ampere (A). 1 Ampere = 1 Coulomb / 1 second.
- Nature: It's a scalar quantity, although it has a direction (conventionally, the direction of flow of positive charge, opposite to the flow of electrons).
- Current Carriers:
- Metals: Free electrons
- Electrolytes: Positive and negative ions
- Semiconductors: Electrons and holes
2. Drift Velocity (v<0xE1><0xB5><0xA2>) and Current
- Concept: In a conductor without an electric field, electrons move randomly with high thermal velocities, but the net flow is zero. When an electric field (E) is applied, electrons drift slowly in the direction opposite to E. This average velocity is called drift velocity.
- Relation between Current and Drift Velocity: I = n e A v<0xE1><0xB5><0xA2>
- n = number density of free electrons (number of free electrons per unit volume)
- e = charge of an electron (1.6 x 10⁻¹⁹ C)
- A = cross-sectional area of the conductor
- v<0xE1><0xB5><0xA2> = drift velocity
- Drift Velocity Formula: v<0xE1><0xB5><0xA2> = (e E / m) τ
- m = mass of electron
- τ = average relaxation time (average time between successive collisions)
- Mobility (μ): Drift velocity acquired per unit electric field. μ = v<0xE1><0xB5><0xA2> / E = (e τ / m). SI Unit: m² V⁻¹ s⁻¹
3. Ohm's Law
- Statement: Provided the physical conditions (like temperature, pressure) remain unchanged, the current (I) flowing through a conductor is directly proportional to the potential difference (V) across its ends.
- Formula: V ∝ I => V = R I
- Resistance (R): The opposition offered by the conductor to the flow of current. R = V / I.
- SI Unit of Resistance: Ohm (Ω). 1 Ohm = 1 Volt / 1 Ampere.
- Limitations: Ohm's law is not universally applicable. Devices that do not obey Ohm's law are called non-ohmic devices (e.g., semiconductor diodes, transistors, electrolytes). Their V-I graph is not a straight line passing through the origin.
4. Resistance (R) and Resistivity (ρ)
- Factors Affecting Resistance:
- Length (l): R ∝ l
- Cross-sectional Area (A): R ∝ 1/A
- Nature of Material: Depends on resistivity (ρ)
- Temperature
- Formula: R = ρ (l / A)
- Resistivity (ρ) or Specific Resistance: Resistance of a conductor of unit length and unit cross-sectional area. It depends only on the nature of the material and temperature, not on the dimensions of the conductor.
- SI Unit of Resistivity: Ohm-meter (Ω m).
- Conductance (G): Reciprocal of resistance. G = 1/R. SI Unit: Siemens (S) or mho (Ω⁻¹).
- Conductivity (σ): Reciprocal of resistivity. σ = 1/ρ. SI Unit: Siemens per meter (S m⁻¹) or Ω⁻¹ m⁻¹.
- Vector Form of Ohm's Law: J = σ E (where J is Current Density, J = I/A, a vector quantity).
5. Temperature Dependence of Resistance
- Metals: Resistance increases with increasing temperature. As temperature rises, ions vibrate more vigorously, increasing the frequency of collisions for electrons, thus reducing relaxation time (τ) and increasing resistance.
- Formula: R<0xE2><0x82><0x9C> = R₀ [1 + α(T - T₀)]
- ρ<0xE2><0x82><0x9C> = ρ₀ [1 + α(T - T₀)]
- α = temperature coefficient of resistance (positive for metals).
- Semiconductors & Insulators: Resistance decreases with increasing temperature. Increased temperature provides energy to break covalent bonds, increasing the number density (n) of charge carriers significantly, which outweighs the effect of decreased relaxation time. (α is negative).
- Alloys (like Manganin, Constantan): Have very small temperature coefficients of resistance and high resistivity. Used for making standard resistance coils.
6. Electrical Energy and Power
- Electrical Energy (W or E): Work done by the source to maintain current in a circuit.
- W = V I t = I² R t = (V² / R) t
- SI Unit: Joule (J). Commercial Unit: kilowatt-hour (kWh) or Board of Trade (BOT) unit. 1 kWh = 3.6 x 10⁶ J.
- Electrical Power (P): The rate at which electrical energy is consumed or work is done.
- P = W / t = V I = I² R = V² / R
- SI Unit: Watt (W). 1 Watt = 1 Joule / 1 second.
7. Combination of Resistors
- Series Combination:
- Resistors connected end-to-end.
- Same current flows through each resistor.
- Voltage divides across resistors (V = V₁ + V₂ + ...).
- Equivalent Resistance (R<0xE2><0x82><0x9B>): R<0xE2><0x82><0x9B> = R₁ + R₂ + R₃ + ...
- R<0xE2><0x82><0x9B> is always greater than the largest individual resistance.
- Parallel Combination:
- Resistors connected between the same two points.
- Same voltage across each resistor.
- Current divides through resistors (I = I₁ + I₂ + ...).
- Equivalent Resistance (R<0xE2><0x82><0x9A>): 1/R<0xE2><0x82><0x9A> = 1/R₁ + 1/R₂ + 1/R₃ + ...
- For two resistors: R<0xE2><0x82><0x9A> = (R₁ R₂) / (R₁ + R₂)
- R<0xE2><0x82><0x9A> is always smaller than the smallest individual resistance.
8. Cells, EMF (E), Internal Resistance (r), and Terminal Potential Difference (V)
- Electromotive Force (EMF - E): The potential difference across the terminals of a cell when no current is drawn from it (open circuit). It represents the maximum potential difference the cell can provide. Unit: Volt (V).
- Internal Resistance (r): The opposition offered by the electrolyte and electrodes of the cell to the flow of current within the cell. Unit: Ohm (Ω).
- Terminal Potential Difference (V): The potential difference across the terminals of a cell when current is being drawn from it (closed circuit).
- Relationship:
- When discharging (cell supplying current): V = E - I r
- When charging (current forced into positive terminal): V = E + I r
- In open circuit (I=0): V = E
9. Combination of Cells
- Series Combination:
- Connect negative terminal of one to positive terminal of the next.
- Equivalent EMF: E<0xE2><0x82><0x91><0xE2><0x82><0x9A> = E₁ + E₂ + ... (If connected in aiding manner) or E<0xE2><0x82><0x91><0xE2><0x82><0x9A> = |E₁ - E₂| (if opposing).
- Equivalent Internal Resistance: r<0xE2><0x82><0x91><0xE2><0x82><0x9A> = r₁ + r₂ + ...
- Useful when external resistance (R) is much larger than total internal resistance (R >> r<0xE2><0x82><0x91><0xE2><0x82><0x9A>).
- Parallel Combination (Identical Cells):
- Connect all positive terminals together and all negative terminals together.
- Equivalent EMF: E<0xE2><0x82><0x91><0xE2><0x82><0x9A> = E (EMF of a single cell)
- Equivalent Internal Resistance: 1/r<0xE2><0x82><0x91><0xE2><0x82><0x9A> = 1/r₁ + 1/r₂ + ... => r<0xE2><0x82><0x91><0xE2><0x82><0x9A> = r/n (for n identical cells)
- Useful when external resistance (R) is much smaller than total internal resistance (R << r<0xE2><0x82><0x91><0xE2><0x82><0x9A>).
- (Note: Formula for non-identical cells in parallel is more complex and less common in basic exams).
10. Kirchhoff's Laws (For Complex Circuits)
- Kirchhoff's First Law (Junction Rule or KCL - Kirchhoff's Current Law): The algebraic sum of currents meeting at any junction in an electrical circuit is zero (ΣI = 0).
- Basis: Conservation of Charge.
- Convention: Currents entering a junction are positive, currents leaving are negative (or vice-versa, be consistent).
- Kirchhoff's Second Law (Loop Rule or KVL - Kirchhoff's Voltage Law): The algebraic sum of changes in potential around any closed loop involving resistors and cells is zero (ΣΔV = 0).
- Basis: Conservation of Energy.
- Convention (while traversing a loop):
- Potential drop across a resistor in the direction of current: -IR
- Potential rise across a resistor opposite to the direction of current: +IR
- Potential rise when moving from negative to positive terminal of a cell: +E
- Potential drop when moving from positive to negative terminal of a cell: -E
11. Wheatstone Bridge
- Principle: An arrangement of four resistances used to measure one unknown resistance accurately in terms of the other three.
- Circuit: Four resistors (P, Q, R, S) form a quadrilateral. A galvanometer (G) is connected between one pair of opposite junctions, and a cell between the other pair.
- Balanced Condition: When the potential difference across the galvanometer is zero (i.e., no current flows through it, I<0xE1><0xB5><0x8A> = 0), the bridge is said to be balanced.
- Balance Condition: P / Q = R / S
- Application: Used to find an unknown resistance (e.g., if S is unknown, S = R * (Q/P)). Highly sensitive when all four resistances are of comparable magnitude.
12. Metre Bridge (Slide Wire Bridge)
- Principle: Practical application of the Wheatstone bridge. Works on the principle of a balanced Wheatstone bridge.
- Construction: Consists of a uniform wire (usually 1m long, made of manganin or constantan) stretched over a scale. Known resistance (R) and unknown resistance (S) are connected in two gaps. A galvanometer is connected to a sliding jockey.
- Working: The jockey is moved along the wire until the galvanometer shows zero deflection (balance point). If the balance point is at length l₁ from one end (say, connected to R), then the length corresponding to S is l₂ = (100 - l₁).
- Formula: R / S = (Resistance of length l₁) / (Resistance of length l₂) = (ρ l₁ / A) / (ρ l₂ / A) = l₁ / l₂
=> S = R (l₂ / l₁) = R (100 - l₁) / l₁ - Sources of Error: Non-uniformity of the wire, end corrections (resistance at the connection points), heating effects.
13. Potentiometer
- Principle: When a constant current flows through a wire of uniform cross-sectional area and composition, the potential drop across any length of the wire is directly proportional to that length (V ∝ l).
- V = k l, where k is the potential gradient (potential drop per unit length). k = V<0xE1><0xB5><0xAB><0xE1><0xB5><0xA2><0xE1><0xB5><0xA8> / L (where L is the total length of the potentiometer wire).
- Superiority over Voltmeter: A potentiometer measures the true EMF of a cell (or potential difference) accurately because it draws no current from the source at the balance point (null deflection method). A voltmeter always draws some current, hence measures V = E - Ir, which is less than E.
- Applications:
- Comparison of EMFs of two cells: E₁ / E₂ = l₁ / l₂ (where l₁ and l₂ are the balancing lengths for cells E₁ and E₂ respectively).
- Measurement of Internal Resistance of a cell: r = R ( (l₁ - l₂) / l₂ )
- l₁ = balancing length when the cell is in open circuit (only cell E connected).
- l₂ = balancing length when a known resistance (R) is connected across the cell (cell is discharging).
Key Points to Remember for Exams:
- Distinguish between EMF and Terminal Potential Difference.
- Understand the conditions under which Ohm's Law is valid and where it fails.
- Know the factors affecting resistance and resistivity.
- Be comfortable applying Kirchhoff's Laws to solve circuit problems.
- Understand the principle and working of Wheatstone Bridge, Metre Bridge, and Potentiometer.
- Remember the formulas for series and parallel combinations (resistors and cells).
- Practice numerical problems based on these concepts.
Multiple Choice Questions (MCQs)
-
The resistivity of a metallic conductor depends on:
(a) Length of the conductor
(b) Area of cross-section of the conductor
(c) Temperature of the conductor
(d) Dimensions of the conductor -
Kirchhoff's junction rule (KCL) is a consequence of the conservation of:
(a) Energy
(b) Momentum
(c) Charge
(d) Mass -
In a balanced Wheatstone bridge, if the positions of the cell and galvanometer are interchanged, the balance condition will:
(a) Change
(b) Remain unchanged
(c) Become P/Q = S/R
(d) Depend on the internal resistance of the cell -
A potentiometer is preferred over a voltmeter for measuring the EMF of a cell because:
(a) It is more sensitive.
(b) It does not draw any current from the cell at balance point.
(c) It has a wire of high resistance.
(d) It uses a galvanometer for null detection. -
The drift velocity v<0xE1><0xB5><0xA2> varies with the intensity of the electric field E as per the relation:
(a) v<0xE1><0xB5><0xA2> ∝ E²
(b) v<0xE1><0xB5><0xA2> ∝ E
(c) v<0xE1><0xB5><0xA2> ∝ 1/E
(d) v<0xE1><0xB5><0xA2> is independent of E -
Two resistors R₁ and R₂ are connected in parallel. The equivalent resistance R<0xE2><0x82><0x9A> is:
(a) R<0xE2><0x82><0x9A> > R₁ + R₂
(b) R<0xE2><0x82><0x9A> < R₁ and R<0xE2><0x82><0x9A> < R₂
(c) R<0xE2><0x82><0x9A> = (R₁ + R₂) / 2
(d) R<0xE2><0x82><0x9A> lies between R₁ and R₂ -
When the temperature of a semiconductor is increased, its resistance:
(a) Decreases
(b) Increases
(c) Remains unchanged
(d) First increases then decreases -
A cell of EMF 'E' and internal resistance 'r' is connected across an external resistance 'R'. The terminal potential difference 'V' across the cell is given by:
(a) V = E + Ir
(b) V = E - Ir
(c) V = E
(d) V = Ir -
The SI unit of electrical conductivity is:
(a) Ohm (Ω)
(b) Ohm-meter (Ω m)
(c) Siemens (S)
(d) Siemens per meter (S m⁻¹) -
In a metre bridge experiment, the balance point is found at length l₁ from the end corresponding to the known resistance R. The unknown resistance S is given by:
(a) S = R (l₁ / (100 - l₁))
(b) S = R ((100 - l₁) / l₁)
(c) S = R (l₁ / 100)
(d) S = R (100 / l₁)
Answers to MCQs:
- (c) Temperature of the conductor
- (c) Charge
- (b) Remain unchanged
- (b) It does not draw any current from the cell at balance point.
- (b) v<0xE1><0xB5><0xA2> ∝ E
- (b) R<0xE2><0x82><0x9A> < R₁ and R<0xE2><0x82><0x9A> < R₂
- (a) Decreases
- (b) V = E - Ir (Assuming the cell is discharging, which is the usual case when connected to external R)
- (d) Siemens per meter (S m⁻¹)
- (b) S = R ((100 - l₁) / l₁)
Make sure you thoroughly understand these concepts and practice solving problems based on them. Good luck with your preparation!