Chapter 11: Electricity

1. Electric Current and Electric Circuit

Electric current is the rate of flow of electric charge. I = Q/t. Its SI unit is ampere (A).

An electric circuit is a continuous and closed conducting path through which current can flow. By convention, current is taken in the direction of positive charge flow; electrons in metals move in the opposite direction.

2. Electric Potential and Potential Difference

Potential difference between two points is the work done to move a unit charge from one point to another: V = W/Q. Its SI unit is volt (V). A cell or battery provides the potential difference that drives current in a circuit.

3. Circuit Components and Measuring Instruments

4. Ohm's Law

For a conductor at constant temperature, potential difference is directly proportional to current: V ∝ I, hence V = IR. Therefore R = V/I. Resistance is measured in ohms (Ω).

For an ohmic conductor at constant temperature, the V–I graph is a straight line through the origin. On a V-versus-I graph, its slope gives resistance.

5. Factors Affecting Resistance

Resistance depends on length, area of cross-section, material and temperature. For a uniform conductor, R = ρl/A.

• Greater length → greater resistance.
• Greater cross-sectional area → lower resistance.
• Different materials have different resistivities.
• Temperature can change resistance.

6. Resistivity

Resistivity (ρ) is a property of the material. ρ = RA/l. Its SI unit is Ω m. For a specified material and temperature, resistivity does not depend on the dimensions of the particular wire.

7. Resistance in Series

In series, the same current flows through every resistor. Rₛ = R₁ + R₂ + R₃ + …. The total potential difference is the sum of individual potential differences. Equivalent resistance is greater than each individual resistance.

8. Resistance in Parallel

In parallel, the same potential difference acts across every branch. 1/Rₚ = 1/R₁ + 1/R₂ + 1/R₃ + …. Total current is the sum of branch currents. Equivalent resistance is less than the smallest branch resistance.

For two resistors: Rₚ = R₁R₂/(R₁ + R₂).

9. Why Household Circuits Use Parallel Connection

• Each appliance receives the supply potential difference.
• Appliances can be operated independently.
• Failure of one branch normally does not stop other branches.
• Different appliances can draw different currents according to their resistances and ratings.

10. Heating Effect of Electric Current

When current passes through a resistor, electrical energy is converted into heat. This is the heating effect.

H = I²Rt = VIt = V²t/R.

Applications include electric iron, heater, toaster, kettle and electric fuse. Nichrome is commonly used for heating elements because it has suitable resistance and a high melting point.

11. Electric Power and Energy

Power is the rate at which electrical energy is consumed: P = W/t = VI = I²R = V²/R. SI unit: watt (W).

Electrical energy: E = Pt. The commercial unit is kilowatt-hour (kWh). 1 kWh = 3.6 × 10⁶ J.

12. Solved Numericals

Example 1

6 V across 3 Ω: I = V/R = 6/3 = 2 A.

Example 2

2 Ω and 4 Ω in series: R = 6 Ω. Across 12 V, I = 12/6 = 2 A.

Example 3

6 Ω and 3 Ω in parallel: 1/R = 1/6 + 1/3 = 1/2, so R = 2 Ω.

Example 4

220 V and 2 A: P = VI = 440 W.

Example 5

1 kW for 3 hours: E = 3 kWh = 1.08 × 10⁷ J.

13. Series vs Parallel

14. Formula Bank

15. Quick Revision – One Look

• I = Q/t
• V = W/Q
• V = IR
• R = ρl/A
• Series: same current; resistances add.
• Parallel: same potential difference; reciprocal resistances add.
• H = I²Rt
• P = VI = I²R = V²/R
• E = Pt
• 1 kWh = 3.6 × 10⁶ J

16. 30 Practice Questions

1. Define electric current and write its SI unit.
2. Write the relation between charge, current and time.
3. Define one ampere.
4. What is an electric circuit?
5. Define potential difference.
6. State Ohm's law.
7. Define resistance and give its SI unit.
8. Describe the V–I graph for an ohmic conductor.
9. State two factors affecting resistance.
10. Write the relation between resistance and resistivity.
11. Define resistivity and state its SI unit.
12. Why does a longer wire generally have greater resistance?
13. Why does a thick wire generally have lower resistance?
14. Why is an ammeter connected in series?
15. Why is a voltmeter connected in parallel?
16. Find equivalent resistance of 2 Ω, 3 Ω and 5 Ω in series.
17. Find equivalent resistance of 6 Ω and 3 Ω in parallel.
18. State two advantages of parallel connection.
19. Define heating effect of electric current.
20. Write three expressions for heat produced.
21. State two applications of heating effect.
22. Define electric power.
23. Write three formulae for electric power.
24. Define one watt.
25. What is electrical energy?
26. Define one kilowatt-hour.
27. Convert 2 kWh into joules.
28. A 12 V source is connected to 4 Ω. Find current.
29. A device draws 5 A from 220 V. Find power.
30. A 1000 W appliance works for 2 hours. Find energy in kWh.

17. 20 CBSE PYQ / PYQ-Based Questions

Exam-oriented questions based on the chapter and CBSE-style competency practice. They are not presented as verbatim copies of official papers.

1. An ammeter is connected in parallel and a voltmeter in series. Identify the mistakes and give the correct connections.
2. State Ohm's law and its mathematical form.
3. How does resistance change when the length of a wire is doubled?
4. How does resistance change when area of cross-section is doubled?
5. Define resistivity and state its SI unit.
6. 4 Ω and 6 Ω are in series across 20 V. Calculate current.
7. 6 Ω and 3 Ω are in parallel. Calculate equivalent resistance.
8. Why are household appliances connected in parallel?
9. Derive the equivalent resistance of resistors in series.
10. Derive the equivalent resistance of resistors in parallel.
11. A bulb is rated 220 V, 100 W. Find current at rated voltage.
12. An appliance consumes 2 kW for 3 hours. Find energy in kWh and joules.
13. State Joule's law of heating.
14. Why is nichrome used in heating elements?
15. Distinguish between electric power and electrical energy.
16. A resistor carries 2 A at 10 V. Find resistance.
17. 2 Ω, 4 Ω and 6 Ω are in series across 24 V. Find total resistance and current.
18. 2 Ω, 3 Ω and 6 Ω are in parallel. Find equivalent resistance.
19. Explain why an incandescent bulb filament becomes hot.
20. A 20 Ω device is connected to 10 V. Calculate current and power.

18. Interactive MCQ Quiz – 20 Questions

Select one option for each question and click Check Score.