Chapter 11: Electricity

Electric current and potential difference

Electric current I = Q/t (unit ampere). Potential difference V = W/Q (unit volt). Ohm's law: at constant temperature V = IR. The unit of resistance is the ohm.

R = ρ l / A (length l, area A, resistivity ρ)

Combination of resistors

Series: same current, Rs = R₁ + R₂ + R₃. Parallel: same potential difference, 1/Rp = 1/R₁ + 1/R₂ + 1/R₃. Household appliances are connected in parallel. An ammeter is connected in series and a voltmeter in parallel.

Heating effect of electric current

Joule's law: H = I²Rt. Electric heaters, irons and bulbs work on this. Tungsten, which has a high melting point, is used for bulb filaments. The wire of a fuse has a low melting point.

Electric power and energy

P = VI = I²R = V²/R (unit watt). Energy = power × time. The commercial unit of electrical energy is the kilowatt-hour (kWh), also called one unit. 1 kWh = 3.6 × 10⁶ J.

Important questions

Q1. Define electric current.

The rate of flow of charge: I = Q/t. Its SI unit is the ampere (A).

Q2. What is 1 ampere?

When 1 coulomb of charge flows through a conductor in 1 second.

Q3. What is potential difference? Define 1 volt.

The work done in moving a unit charge from one point to another: V = W/Q. 1 volt = 1 joule per coulomb.

Q4. State Ohm's law.

At constant temperature, the potential difference across a conductor is directly proportional to the current through it: V = IR.

Q5. What is resistance? What is its unit?

The property of a conductor that opposes the flow of current. Its unit is the ohm (Ω). A resistance is 1 Ω when 1 A flows at a potential difference of 1 V.

Q6. On what factors does the resistance of a conductor depend?

On its length, area of cross-section, material and temperature: R = ρl/A.

Q7. What is resistivity?

The resistance of a conductor of unit length and unit area of cross-section. Its unit is Ω m and it depends on the material and temperature.

Q8. A bulb draws 0.5 A at 220 V. What is its resistance?

R = V/I = 220/0.5 = 440 Ω.

Q9. A charge of 10 C flows through a wire in 5 s. Find the current.

I = Q/t = 10/5 = 2 A.

Q10. How much work is done in moving a charge of 2 C across a potential difference of 12 V?

W = QV = 2 × 12 = 24 J.

Q11. What is the equivalent resistance of resistors in series?

Rs = R1 + R2 + R3 ... The same current flows through all of them and the potential difference gets divided.

Q12. What is the equivalent resistance of resistors in parallel?

1/Rp = 1/R1 + 1/R2 + 1/R3 ... The potential difference is the same across all of them and the current gets divided.

Q13. Find the equivalent resistance of 3 Ω and 6 Ω resistors (a) in series (b) in parallel.

(a) 3 + 6 = 9 Ω. (b) 1/Rp = 1/3 + 1/6 = 1/2, so Rp = 2 Ω.

Q14. Why are household appliances connected in parallel?

So that each appliance gets the same potential difference, can be switched on and off separately, and the others keep working if one fails.

Q15. State Joule's law of heating.

H = I²Rt, that is, the heat produced is proportional to the square of the current, the resistance and the time.

Q16. Write the formulae for electric power.

P = VI = I²R = V²/R. Its unit is the watt (W).

Q17. How much energy is used when a 100 W bulb burns for 5 hours?

Energy = 0.1 kW × 5 h = 0.5 kWh, that is 0.5 unit.

Q18. How many joules make 1 kWh?

3.6 × 10⁶ J.

Q19. Why is tungsten used for the filament of a bulb?

It has a very high melting point (about 3380 °C) and high resistivity, so it does not melt even when it becomes very hot.

Q20. How are an ammeter and a voltmeter connected in a circuit?

An ammeter is connected in series (it has low resistance) and a voltmeter is connected in parallel (it has high resistance).

Quiz

1. What is the SI unit of electric current?

2. What current flows when 12 V is applied across a 4 Ω resistor?

3. Resistors of 2 Ω and 3 Ω are connected in series. What is the equivalent resistance?

4. How many joules make 1 kWh?

5. Which quantity remains the same in a parallel combination?

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