Exercise Solutions Available
Step-by-step answers for all textbook questions in this chapter
Board Exam Weight: Current Electricity carries 8–10 marks in Tamil Nadu Class 12 Physics board exams (Volume 1, Chapter 2). NEET typically has 2–4 questions from this chapter.
1. Electric Current and Drift Velocity
Electric current I is the rate of flow of charge:
Drift velocity v_d is the average velocity of free electrons in the direction opposite to the electric field:
where n = number density of free electrons, A = cross-sectional area, e = 1.6×10⁻¹⁹ C.
2. Ohm's Law — Two Forms
Macroscopic Form
Valid when temperature is constant and the conductor is ohmic (linear V-I graph).
Microscopic Form (Ohm's Law in terms of field quantities)
where:
- J = current density = I/A (A/m²)
- σ = electrical conductivity (Ω⁻¹·m⁻¹ or S/m)
- E = electric field inside conductor (V/m)
Resistivity ρ = 1/σ, so: J = E/ρ → E = ρJ
Resistance from resistivity:
where L = length, A = cross-sectional area.
Temperature Dependence of Resistance
For most metals, resistance increases with temperature:
where α is the temperature coefficient of resistance (unit: K⁻¹ or °C⁻¹).
3. Kirchhoff's Laws
KCL — Kirchhoff's Current Law (Junction Rule)
"The algebraic sum of currents at any junction is zero."
Based on conservation of charge.
KVL — Kirchhoff's Voltage Law (Loop Rule)
"The algebraic sum of all potential differences (EMF and IR drops) around any closed loop is zero."
Based on conservation of energy.
Sign conventions for KVL:
- Traversing a resistor in the direction of assumed current: voltage drop = −IR
- Traversing a battery from − to +: gain = +E
- Traversing a battery from + to −: drop = −E
4. Wheatstone Bridge
Four resistors P, Q, R, S arranged in a bridge circuit with a galvanometer connecting the midpoints.
Balanced condition (no current through galvanometer):
To find unknown resistance S:
Uses: Finding unknown resistance with high accuracy. Metre bridge is a practical form.
5. Metre Bridge
A practical form of the Wheatstone bridge using a 1-metre uniform resistance wire.
Principle:
If balancing length is l cm from left end (for resistance R in left gap and unknown S in right gap):
Precautions:
- Jockey should be tapped gently — not dragged
- Null point should be near the middle of wire (40–60 cm) for accuracy
- Connections should be tight to avoid contact resistance
6. Potentiometer
A long uniform resistance wire used to make precise voltage and EMF measurements.
Principle: When no current is drawn from the cell, the potential drop across a length l of wire is proportional to l:
where φ = potential gradient = V_total / L_wire (V/m).
Applications
7. EMF and Internal Resistance
Every real battery has internal resistance r. When current I flows:
Power delivered to external circuit:
Power dissipated internally:
Maximum power theorem: Power delivered to external R is maximum when R = r (internal resistance).
8. Worked Numericals
Numerical 1 — KVL Circuit Problem
Problem: A circuit has a 12 V battery (negligible internal resistance) with three resistors 3 Ω, 4 Ω, and 5 Ω connected in series. Find the current and voltage across each resistor.
Numerical 2 — Wheatstone Bridge
Problem: In a Wheatstone bridge, P = 10 Ω, Q = 15 Ω, R = 20 Ω. Find the value of S for balance.
The unknown resistance S = 30 Ω.
Numerical 3 — Internal Resistance
Problem: A battery of EMF 6 V and internal resistance 0.5 Ω is connected to an external resistance of 11.5 Ω. Find: (a) current in the circuit, (b) terminal voltage of the battery.
Terminal voltage (5.75 V) is less than EMF (6 V) because of the voltage drop across internal resistance.
Numerical 4 — Potentiometer (Comparing EMFs)
Problem: In a potentiometer experiment, a standard cell of 2.0 V gives a balancing length of 400 cm. An unknown cell gives a balancing length of 300 cm. Find the EMF of the unknown cell.
The EMF of the unknown cell is 1.5 V.
9. Board Exam Model Questions
2-Mark Questions
Q1. State Kirchhoff's voltage law and give its physical basis. KVL: The algebraic sum of all EMFs and potential drops around any closed loop in a circuit equals zero. Physical basis: conservation of energy — a charge completing a closed loop returns to the same potential, so net work done is zero.
Q2. Define potential gradient in a potentiometer. Give its SI unit. Potential gradient is the potential drop per unit length of the potentiometer wire: φ = V/L. It is uniform along the wire if the wire has uniform cross-section and material. SI unit: V/m (or V/cm in practice).
Q3. Why is a potentiometer preferred over a voltmeter for measuring EMF? A potentiometer draws no current from the cell at the null point (balance condition), so it measures the true EMF without any terminal voltage drop. A voltmeter, having finite resistance, draws current and measures terminal voltage (V = E − Ir), which is less than the true EMF.
5-Mark Questions
10. NEET Relevance
| Topic | NEET Frequency |
|---|---|
| Ohm's law — resistivity, drift velocity | High |
| Kirchhoff's laws — circuit solving | Very High |
| Wheatstone bridge | High |
| Potentiometer — comparing EMFs | Medium |
| Internal resistance — terminal voltage | Very High |
| Combination of resistors | Very High |
NEET Tip: Practice multi-loop KVL problems. NEET often gives a circuit with two loops and asks for current through a specific element — apply KVL systematically to each loop.
11. Key Formulae Summary
| Quantity | Formula |
|---|---|
| Current | I = Q/t = nAev_d |
| Ohm's law | V = IR, J = σE |
| Resistivity | R = ρL/A |
| KCL | ΣI_in = ΣI_out |
| KVL | ΣE = ΣIR (around loop) |
| Wheatstone balance | P/Q = R/S |
| Metre bridge | S = R(100−l)/l |
| Potentiometer (EMFs) | E₁/E₂ = l₁/l₂ |
| Internal resistance | V = E − Ir |
| Internal r (potentiometer) | r = R(l₁−l₂)/l₂ |
Constants: e = 1.6×10⁻¹⁹ C