Unit 4
Electricity and Magnetism
Class 11 Physics
Chapter 23
DC Circuits
Class 11 Physics – DC Circuits Notes PDF
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Chapter Overview
Direct-current circuits describe the steady flow of electric charge through conductors and circuit components. The chapter connects the microscopic motion of charge carriers with measurable quantities such as current, resistance, voltage, electromotive force and electrical power.
The official scope includes electric current and drift velocity, Ohm’s law, resistance/resistivity/conductivity, current–voltage characteristics, series and parallel resistors, potential dividers, electromotive force with internal resistance, and electrical work and power.
23.1 Electric Current and Drift Velocity
Electric Current
Electric current is the rate of flow of electric charge through a cross-section of a conductor.
The SI unit is the ampere (A), where 1 A = 1 C s−1.
Conventional Current and Electron Flow
Conventional current is defined in the direction positive charge would move. In metallic conductors, electrons drift in the opposite direction.
Diagram 1 — Conventional Current and Electron Drift
In a metal, electron drift is opposite to the conventional-current direction.
Drift Velocity
Without an electric field, conduction electrons move randomly and have no net average motion. When an electric field is applied, they acquire a small average drift velocity vd.
In time t, charge carriers within a cylinder of length vdt cross area A. If n is the number of free charge carriers per unit volume and q is the magnitude of charge per carrier:
For electrons, q = e in magnitude:
Diagram 2 — Drift-Velocity Derivation
Current equals the charge density per unit volume times cross-sectional area and drift speed.
23.2 Ohm’s Law, Resistance, Resistivity and Conductivity
Ohm’s Law
For an ohmic conductor maintained at constant physical conditions, current is directly proportional to potential difference:
Resistance is:
Resistance of a Uniform Conductor
where ρ is resistivity, L is length and A is cross-sectional area.
Resistivity is a material property with SI unit Ω m. Conductivity σ is the reciprocal:
| Quantity | Symbol | Depends mainly on | SI unit |
|---|---|---|---|
| Resistance | R | Material, length, area, temperature | Ω |
| Resistivity | ρ | Material and temperature | Ω m |
| Conductivity | σ | Material and temperature | S m⁻¹ |
Diagram 3 — Factors Affecting Resistance
For the same material and temperature, increasing length increases resistance while increasing area lowers it.
23.3 Current–Voltage Characteristics: Ohmic and Non-Ohmic Devices
An ohmic conductor has a linear V–I relation over the range where its physical conditions stay constant. A non-ohmic device does not maintain a constant V/I ratio.
Diagram 4 — Ohmic and Non-Ohmic I–V Characteristics
A straight line through the origin indicates constant resistance; a curved characteristic indicates resistance varies with operating conditions.
23.4 Resistors in Series and Parallel
Series Combination
The same current flows through all series resistors, while potential differences add:
Diagram 5 — Resistors in Series
Series resistance is greater than any individual resistance.
Parallel Combination
Each branch has the same potential difference, while currents add:
For two resistors:
Diagram 6 — Resistors in Parallel
Parallel equivalent resistance is less than the smallest branch resistance.
23.5 Potential Divider
A potential divider uses resistors in series to obtain a chosen fraction of an applied voltage.
For R₁ and R₂ in series across Vin, with Vout taken across R₂ and with negligible loading:
Diagram 7 — Potential Divider
With no significant load attached, the output voltage is the fraction of the total voltage appearing across R₂.
23.6 Electromotive Force and Internal Resistance
Electromotive Force
The electromotive force (emf) ε of a source is the energy supplied by the source per unit charge around the complete circuit:
Despite its name, emf is measured in volts and is not a force.
Internal Resistance
A real source has internal resistance r. If current I is delivered to an external load R:
The terminal potential difference while the source delivers current is:
Diagram 8 — Real Cell with Internal Resistance
Part of the source emf is lost across internal resistance when current flows.
23.7 Work and Power in Electrical Circuits
When charge Q moves through potential difference V, electrical work is:
Since Q = It:
Electrical power is:
For a resistor using V = IR:
Electrical energy dissipated in time t is:
| Quantity | Formula | SI unit |
|---|---|---|
| Electrical work / energy | W = VIt | J |
| Power | P = VI | W |
| Resistive power | P = I²R = V²/R | W |
Solved Numerical Examples
Example 1 — Drift Velocity
Question: A wire carries 2.0 A. If n = 8.5×10²⁸ m⁻³, A = 1.0×10⁻⁶ m² and e = 1.60×10⁻¹⁹ C, find vd.
Answer: about 1.5×10⁻⁴ m s⁻¹.
Example 2 — Resistance
Question: A wire has ρ = 1.7×10⁻⁸ Ωm, L = 2.0 m and A = 1.0×10⁻⁶ m². Find R.
Answer: 0.034 Ω.
Example 3 — Series and Parallel
Question: Find the equivalent resistance of 6 Ω and 3 Ω in parallel.
Answer: 2 Ω.
Example 4 — Potential Divider
Question: R₁ = 2 kΩ and R₂ = 3 kΩ are connected across 10 V. Find the unloaded Vout across R₂.
Answer: 6 V.
Example 5 — Internal Resistance
Question: A cell of emf 1.5 V and internal resistance 0.20 Ω supplies 1.0 A. Find terminal voltage.
Answer: 1.30 V.
Example 6 — Electrical Power
Question: A 12 V lamp draws 2 A. Find its power.
Answer: 24 W.
Important Exam Questions
Short-Answer Questions
- Define electric current and write its SI unit.
- Distinguish conventional current from electron drift.
- Define drift velocity.
- State Ohm’s law.
- Differentiate resistance and resistivity.
- Define conductivity.
- Distinguish ohmic and non-ohmic resistance.
- State the equivalent-resistance relations for series and parallel circuits.
- What is a potential divider?
- Define emf in terms of energy per unit charge.
- What is internal resistance?
- Write the three common power relations for a resistor.
Long-Answer / Derivation Questions
- Derive I = neAvd.
- Explain Ohm’s law and derive R = ρL/A from proportional relationships.
- Derive equivalent resistance for resistors in series and parallel.
- Derive the potential-divider formula.
- Derive V = ε − Ir for a source with internal resistance.
- Derive P = VI, P = I²R and P = V²/R.
Numerical Questions
- Find drift velocity from I, n and A.
- Find resistance from resistivity, length and area.
- Find equivalent resistance of mixed simple series/parallel networks.
- Calculate an unloaded potential-divider output.
- Find current and terminal voltage for a cell with internal resistance.
- Calculate electrical work and power from V, I and t.
Diagram Practice
- Conventional current versus electron drift.
- Drift-velocity cylinder.
- Ohmic and non-ohmic I–V graphs.
- Series and parallel resistor networks.
- Potential divider.
- Real cell with emf and internal resistance.
One-Minute Revision
- I = Q/t for steady current.
- For charge carriers, I = nqAvd.
- Ohm’s law: V = IR under constant physical conditions.
- R = ρL/A.
- σ = 1/ρ.
- Ohmic devices have linear I–V behavior over the relevant range.
- Series: Req = ΣR.
- Parallel: 1/Req = Σ(1/R).
- Potential divider: Vout = VinR₂/(R₁+R₂) when unloaded.
- Emf is source energy supplied per unit charge.
- Terminal voltage while delivering current: V = ε − Ir.
- Electrical work: W = VIt.
- Electrical power: P = VI.
- For a resistor: P = I²R = V²/R.
Syllabus Coverage Checklist
| NEB/CDC Chapter 23 scope | Covered |
|---|---|
| 23.1 Electric currents; drift velocity and relation with current | Yes |
| 23.2 Ohm’s law; resistance; resistivity; conductivity | Yes |
| 23.3 Current–voltage relations; ohmic and non-ohmic resistance | Yes |
| 23.4 Resistances in series and parallel | Yes |
| 23.5 Potential divider | Yes |
| 23.6 Electromotive force and internal resistance | Yes |
| 23.7 Work and power in electrical circuits | Yes |
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