Ch 11Electricity

Chapter 11: Electricity

1. Electric Charge and Electric Current

Electric current is the rate of flow of electric charge through a conductor. In metallic conductors, the current is due to the flow of electrons; however, by convention, the direction of current is taken as the direction of flow of positive charge, i.e. opposite to the direction of electron flow.

• Small currents are expressed in milliampere (1 mA = 10⁻³ A) and microampere (1 μA = 10⁻⁶ A).
• Current is measured by an ammeter, always connected in series in the circuit (it has very low resistance).

Worked reasoning: If 90 C of charge flows through a bulb in 1 minute, then I = Q/t = 90/60 = 1.5 A.

2. Electric Potential and Potential Difference

Potential difference (V) between two points in a circuit is the work done to move a unit positive charge from one point to the other. Charges flow only when there is a potential difference, which is maintained by a cell or battery (using chemical energy).

• Potential difference is measured by a voltmeter, always connected in parallel across the points (it has very high resistance).

Worked reasoning: Work done to move 2 C across 12 V: W = VQ = 12 × 2 = 24 J.

3. Circuit Diagram Symbols

An electric circuit is a continuous and closed path of an electric current. A circuit diagram represents it using standard symbols:

4. Ohm's Law

Statement: The potential difference V across the ends of a metallic conductor is directly proportional to the current I flowing through it, provided its temperature remains constant.

• The graph of V against I is a straight line through the origin; its slope gives R.
• Current is inversely proportional to resistance for a given V: doubling R halves I.
• A rheostat (variable resistance) is used to change the current in a circuit without changing the voltage source.

Worked reasoning: A 12 V battery drives 2.5 mA through a resistor: R = V/I = 12 / (2.5 × 10⁻³) = 4800 Ω = 4.8 kΩ.

5. Factors Affecting Resistance; Resistivity

Resistance is the property of a conductor to oppose the flow of charges through it. It arises because moving electrons collide with the atoms of the conductor. Resistance of a uniform conductor depends on:

1. Length (l): R ∝ l (double the length → double the resistance).
2. Area of cross-section (A): R ∝ 1/A (thicker wire → less resistance).
3. Nature of the material (through resistivity ρ).
4. Temperature: resistance of metals increases with temperature.

• Metals and alloys: ρ ≈ 10⁻⁸ to 10⁻⁶ Ω m (good conductors). Insulators like rubber, glass: ρ ≈ 10¹² to 10¹⁷ Ω m.
• Alloys (nichrome, manganin, constantan) have higher resistivity than pure metals and do not oxidise (burn) readily at high temperatures — hence used in heating elements (electric iron, toaster, heater).
• Copper and aluminium have very low resistivity — used for electrical transmission wires. Tungsten (high melting point) is used for bulb filaments.

6. Combination of Resistors

(a) Resistors in Series

• The same current I flows through each resistor.
• The total potential difference is shared: V = V₁ + V₂ + V₃.

(b) Resistors in Parallel

• The same potential difference V exists across each resistor.
• The total current is shared: I = I₁ + I₂ + I₃.

Why domestic wiring is in parallel: (i) each appliance gets the full supply voltage (220 V); (ii) each appliance can be switched on/off independently; (iii) if one appliance fails, others keep working; (iv) total resistance decreases, so each device draws the current it needs. A series arrangement is impractical because the current would be the same for all devices with different needs, and one failure breaks the whole circuit.

Worked reasoning: Two resistors 6 Ω and 3 Ω in parallel: 1/R_p = 1/6 + 1/3 = 3/6 → R_p = 2 Ω (less than 3 Ω, as expected). In series they would give 9 Ω.

7. Heating Effect of Electric Current

When current flows through a purely resistive conductor, the source's energy is continuously dissipated entirely as heat. This is the heating effect of current (Joule heating).

• Applications: electric iron, heater, toaster, geyser (nichrome element); electric bulb — tungsten filament (melting point 3380 °C) heated to white hot emits light; bulbs are filled with chemically inactive gases (nitrogen, argon) to prolong filament life.
• Electric fuse: safety device in series with the circuit; a wire of an alloy of low melting point that melts and breaks the circuit when current exceeds the safe value (due to overloading or short-circuit). Fuses are rated e.g. 1 A, 2 A, 3 A, 5 A, 10 A.

Worked reasoning: H for 4 A through 20 Ω for 2 s: H = I²Rt = 16 × 20 × 2 = 640 J.

8. Electric Power

Electric power is the rate at which electric energy is dissipated or consumed in a circuit.

Worked reasoning: A 400 W refrigerator running 8 h/day uses 0.4 × 8 = 3.2 kWh per day; at ₹3 per unit for 30 days: cost = 3.2 × 30 × 3 = ₹288.

Rating logic: A bulb marked 220 V, 100 W has R = V²/P = 220²/100 = 484 Ω and draws I = P/V = 100/220 ≈ 0.45 A. A 60 W bulb has a higher resistance (807 Ω) — lower power rating means higher filament resistance at the same voltage.