Electricity and Magnetism

Chapter in a nutshell: Ohm's law ($V=IR$) links voltage, current and resistance; resistors combine in series/parallel. Electrical power ($P=VI$) and energy ($E=Pt$, billed in kWh) run our homes, protected by fuses and earthing. A current creates a magnetic field (basis of the motor, Fleming's left hand), and a changing field induces a current (electromagnetic induction, the generator, Fleming's right hand).

1. Electric Current, Charge & Potential Difference

• Current (I): rate of flow of charge, $I=\dfrac{Q}{t}$; SI unit ampere (A). Conventional current flows from + to −.
• Charge (Q): $Q=It$; unit coulomb (C).
• Potential difference (V): work done per unit charge between two points, $V=\dfrac{W}{Q}$; unit volt (V).

2. Ohm's Law & Resistance

• Resistance (R): opposition to current; unit ohm (Ω).
• Factors: $R=\dfrac{\rho l}{A}$ → R ∝ length (l), R ∝ 1/area (A), depends on material (resistivity ρ) and increases with temperature (for metals).
• Resistivity (ρ): resistance of a unit cube of material; unit Ω m. Good conductors have low ρ.

3. Combination of Resistors

4. EMF, Terminal Voltage & Internal Resistance

• EMF (ε): energy given by the cell per unit charge (measured on open circuit).
• Internal resistance (r): resistance of the cell's electrolyte.
• Terminal voltage: $V = \varepsilon - Ir$ (less than EMF when current flows).

5. Electrical Power & Energy

• Power unit watt (W); energy SI unit joule.
• Commercial unit: kilowatt-hour (kWh) = energy used by a 1 kW appliance in 1 h $= 3.6\times10^{6}$ J ("1 unit").
• Heating effect (Joule's law): $H = I^2Rt$ — basis of heaters, bulbs, fuses.

6. Household Electricity & Safety

• Three wires: Live (L, brown), Neutral (N, blue), Earth (E, green/yellow). Supply ≈ 220 V AC, 50 Hz.
• Fuse / MCB: a thin wire of low-melting alloy placed in the live wire; melts/trips if current exceeds a safe value (protects against short-circuit/overload).
• Earthing: connects the metal body of an appliance to the ground; if the live wire touches the body, current flows safely to earth (or blows the fuse) → prevents shock.
• Appliances are connected in parallel (same voltage, independent on/off, one failing doesn't stop others).
• Overloading (too many appliances) and short-circuiting (live touching neutral) cause excessive current → fire risk → fuse protects.

7. Magnetic Effect of Current (→ the Motor)

• Oersted's experiment: a current-carrying wire deflects a nearby compass → a current produces a magnetic field around it.
• Field of a straight wire = concentric circles (right-hand thumb rule); a solenoid behaves like a bar magnet and forms an electromagnet (strength ↑ with current, turns, soft-iron core).
• Force on a current-carrying conductor in a field — Fleming's Left-Hand Rule (thumb = thrust/force, forefinger = field, centre finger = current). This is the principle of the electric motor (electrical → mechanical energy; uses a split-ring commutator for continuous rotation).

8. Electromagnetic Induction (→ the Generator)

• Faraday's laws: a changing magnetic flux through a coil induces an EMF; the induced EMF ∝ rate of change of flux.
• Lenz's law: the induced current opposes the change causing it (conservation of energy).
• Fleming's Right-Hand Rule gives the direction of the induced current → principle of the generator/dynamo (mechanical → electrical energy). AC generator uses slip rings; DC uses a split-ring commutator.
• Transformer (AC only): changes voltage via $\dfrac{V_s}{V_p}=\dfrac{N_s}{N_p}$; step-up (more secondary turns) for transmission, step-down for use. Works on mutual induction.

9. Worked Numerical Examples (ICSE pattern)

Q2. Three resistors 2 Ω, 3 Ω, 5 Ω in series across 20 V. Find total R and current. Solution: $R_s=2+3+5=10\ \Omega$; $I=V/R=20/10=\mathbf{2\ A}$.

Q3. Two resistors 6 Ω and 3 Ω in parallel. Find the equivalent resistance. Solution: $\dfrac1{R_p}=\dfrac16+\dfrac13=\dfrac12\Rightarrow R_p=\mathbf{2\ \Omega}$.

Q4. An electric bulb is rated 60 W, 220 V. Find its resistance and the current it draws. Solution: $R=\dfrac{V^2}{P}=\dfrac{220^2}{60}=\mathbf{807\ \Omega}$; $I=\dfrac{P}{V}=\dfrac{60}{220}=\mathbf{0.27\ A}$.

Q5. A 1500 W heater runs 4 h daily. Energy used in 30 days (kWh) and cost at ₹5/unit? Solution: daily $=1.5\times4=6$ kWh; 30 days $=180$ kWh; cost $=180\times5=\mathbf{₹900}$.

Q6. A cell of EMF 2 V and internal resistance 0.5 Ω drives 2 A. Find the terminal voltage. Solution: $V=\varepsilon-Ir=2-(2\times0.5)=\mathbf{1\ V}$.

10. Key Terms — Quick Glossary

11. Common Mistakes to Avoid

• Putting the fuse in the neutral wire — it must be in the live wire.
• Mixing up series (same current) and parallel (same voltage).
• Confusing Left-hand rule (motor/force) with Right-hand rule (generator/induced current).
• Treating kW and kWh as the same — kW is power, kWh is energy.
• Forgetting internal resistance: terminal voltage $V=\varepsilon-Ir$, not ε.
• Saying a transformer works on DC — it needs AC (changing flux).

12. Likely Exam Questions (with crisp answers)

1. State Ohm's law. → $V=IR$ at constant temperature.
2. On what factors does the resistance of a wire depend? → Length, area of cross-section, material (resistivity), temperature.
3. Why are household appliances connected in parallel? → Same voltage to each; independent switching; one failing doesn't affect others.
4. Why is a fuse placed in the live wire? → So that on overload it disconnects the live supply, making the appliance safe.
5. What is earthing and why is it done? → Connecting the metal body to earth; provides a safe path for leakage current to prevent shock.
6. State the three equivalent expressions for electrical power. → $P=VI=I^2R=V^2/R$.
7. Define 1 kWh. → Energy used by a 1 kW device in 1 hour ($=3.6\times10^6$ J).
8. State Fleming's Left-Hand Rule and its use. → Thumb=force, forefinger=field, centre finger=current; gives force direction in a motor.
9. State Fleming's Right-Hand Rule and its use. → Gives induced-current direction in a generator.
10. Differentiate a motor and a generator. → Motor: electrical→mechanical (force on current); generator: mechanical→electrical (induced EMF).
11. What is electromagnetic induction? → Production of an EMF by a changing magnetic flux.
12. Why can't a transformer work on DC? → DC gives steady flux (no change) so no EMF is induced in the secondary.
13. Name the energy change in an electric heater / electric motor. → Electrical→heat / electrical→mechanical.
14. State Joule's law of heating. → $H=I^2Rt$.

13. AC vs DC

14. Electromagnet vs Permanent Magnet

15. Parts of a Motor & Generator

• DC motor: armature coil, field magnet, split-ring commutator (reverses current each half-turn for continuous rotation), brushes. Converts electrical → mechanical energy.
• AC generator (dynamo): armature coil rotated in a magnetic field, slip rings + brushes. A changing flux induces an alternating EMF. Converts mechanical → electrical energy.

16. More Worked Numericals

Q8. Find the heat produced in a 10 Ω resistor carrying 2 A for 5 minutes. Solution: $H=I^2Rt=2^2\times10\times300=\mathbf{12000\ J}$.

Q9. Resistors 4 Ω and 12 Ω are in parallel, then in series with 2 Ω across 12 V. Find current from the source. Solution: parallel $=\dfrac{4\times12}{16}=3\ \Omega$; total $=3+2=5\ \Omega$; $I=12/5=\mathbf{2.4\ A}$.

Q10. A transformer has 100 primary turns and 500 secondary turns; input 220 V. Find output voltage (ideal). Solution: $V_s=V_p\dfrac{N_s}{N_p}=220\times\dfrac{500}{100}=\mathbf{1100\ V}$ (step-up).

Q11. An appliance uses 5 A at 220 V. Its power? Solution: $P=VI=220\times5=\mathbf{1100\ W}$.

17. More Exam Questions (with crisp answers)

1. Why is AC preferred for transmission? → It can be stepped up by transformers, reducing $I^2R$ line losses.
2. State Oersted's discovery. → A current-carrying conductor produces a magnetic field around it.
3. How can the strength of an electromagnet be increased? → More turns, larger current, a soft-iron core.
4. Why is soft iron used as the core of an electromagnet? → It is easily magnetised and loses magnetism quickly when current stops.
5. State Lenz's law. → The induced current opposes the change in flux that produces it (energy conservation).
6. What is the function of a commutator in a DC motor? → To reverse the current in the coil every half rotation so it keeps turning the same way.
7. Why does a fuse wire have a low melting point and high resistance? → So it heats up and melts quickly when the current exceeds the safe limit.
8. Name three safety devices in house wiring. → Fuse/MCB, earthing, and switches in the live wire.