Electricity for NDA

Electricity has more one-step numericals than any other NDA physics chapter, and the syllabus covers it widely: static and current electricity, conductors and non-conductors, Ohm's law, simple circuits, the heating, lighting and magnetic effects of current, measurement of electrical power, and primary and secondary cells. The devices list adds the safety fuse and the lightning conductor.

The good news is that almost every numerical uses one of three relations: V = IR, the series and parallel rules, and P = VI with its two variants. If you can move between those quickly, and you know why houses are wired in parallel and why a fuse wire must melt easily, this chapter becomes a reliable source of marks.

Typical question types are:

• charging by rubbing, conductors and insulators, lightning conductors;
• current, charge and the number of electrons;
• Ohm's law and what resistance depends on;
• stretching a wire, and the effect of temperature on resistance;
• equivalent resistance in series and parallel;
• power ratings, brightness of bulbs, and energy bills in kWh;
• fuse, MCB and earthing; materials for filaments and heating elements;
• primary and secondary cells; AC and DC; ammeter and voltmeter connections.

Static electricity

Rubbing two materials transfers electrons from one to the other. A glass rod rubbed with silk becomes positive (it loses electrons); a plastic or ebonite rod rubbed with wool or fur becomes negative. Like charges repel, unlike charges attract. The SI unit of charge is the coulomb, and charge comes in whole-number multiples of the electron's charge, 1.6 × 10⁻¹⁹ C.

• Conductors (metals, graphite, the human body, the earth, impure water) let charge move freely. Insulators (rubber, glass, dry wood, plastic, mica) do not.
• Coulomb's law: the force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.
• Lightning is a huge discharge between charged clouds, or between a cloud and the ground. A lightning conductor is a pointed metal rod on top of a building, connected by a thick strip to a plate buried in the ground; it gives the charge a safe path to earth.
• A closed car is a relatively safe place during lightning because the charge flows over its metal body, not through the inside.

Current and potential difference

Current is the rate of flow of charge: I = Q/t. One ampere is one coulomb per second, which is about 6.25 × 10¹⁸ electrons per second. By convention, current flows from the positive terminal to the negative terminal outside a cell; electrons actually move the other way.

Potential difference is the work done per unit charge in moving it between two points: V = W/Q. One volt is one joule per coulomb. A cell maintains a potential difference; the voltage of a cell on open circuit is its emf.

• An ammeter measures current. It has a low resistance and is connected in series.
• A voltmeter measures potential difference. It has a high resistance and is connected in parallel.
• A galvanometer detects small currents.

Ohm's law and resistance

Ohm's law: at constant temperature, the current through a metallic conductor is proportional to the potential difference across it: V = IR. The resistance R is measured in ohms (Ω). Components that obey this over a range, such as a metal wire at steady temperature, are ohmic. A diode is non-ohmic, and a filament lamp's resistance rises as it heats up.

Resistance R = ρL/A, where L is the length, A the cross-sectional area and ρ the resistivity.

• R is proportional to length and inversely proportional to area. A long thin wire has more resistance than a short thick one.
• Resistivity depends only on the material and the temperature, not on the wire's shape.
• If a wire is stretched to twice its length, its volume stays the same, so its area halves. R becomes 2 × 2 = 4 times.
• The resistance of metals increases with temperature; that of semiconductors decreases. Some materials lose all resistance at very low temperatures (superconductors).

Filament bulbs are filled with an inert gas such as argon or nitrogen to slow the evaporation of the tungsten.

Series and parallel

Shortcuts: n equal resistors R give nR in series and R/n in parallel. Two resistors in parallel give R₁R₂/(R₁ + R₂).

Household appliances are connected in parallel, so that each gets the full mains voltage, draws its own current, and can be switched on or off independently.

Electric power and energy

Power P = VI = I²R = V²/R, in watts. A bulb marked 100 W, 220 V draws 100 W only when run at 220 V. From its rating you can find its resistance: R = V²/P.

Brightness puzzles. Two bulbs rated 100 W and 60 W for the same voltage:

• In parallel (as at home), each gets full voltage and the 100 W bulb glows brighter.
• In series, the same current flows through both; the one with more resistance dissipates more power (I²R). The 60 W bulb has the higher resistance (V²/60 is more than V²/100), so the 60 W bulb glows brighter.

Energy = power × time. The commercial unit is the kilowatt-hour: 1 kWh = 1 "unit" = 3.6 × 10⁶ J.

Bill example (hypothetical rate). A household runs five 100 W bulbs for 6 hours a day for 30 days. Energy = 5 × 0.1 kW × 6 h × 30 = 90 kWh. At ₹6 per unit, the bill for the bulbs is ₹540.

Heating effect and safety

Joule's law of heating: the heat produced in a resistor is H = I²Rt. Heaters, irons, toasters, electric bulbs and fuses all use it.

• A fuse is a short wire of low melting point placed in series with the live wire. If the current exceeds its rating, it melts and breaks the circuit. Its rating must suit the appliance; a thicker fuse wire defeats its purpose.
• An MCB (miniature circuit breaker) does the same job, but it trips like a switch and can simply be reset instead of replaced.
• Overloading means drawing too much current from one socket; a short circuit happens when the live and neutral wires touch, so the resistance becomes almost zero and the current huge. Both are dangers a fuse protects against.
• Earthing: the metal body of an appliance is connected to the earth wire. If the live wire touches the body, the current flows to earth and blows the fuse, instead of passing through a person.
• Household wiring has a live, a neutral and an earth wire. Colour codes vary between old and new standards (the older Indian code is red live, black neutral, green earth), so check the wire, not the colour, in practice.

Cells, AC and DC

• A primary cell cannot be recharged: the common dry cell (Leclanché type, about 1.5 V) in torches and remotes.
• A secondary cell can be recharged: the lead–acid accumulator (about 2 V per cell, so a 12 V car battery has six cells), and nickel–cadmium and lithium-ion cells in phones and laptops.
• Cells in series add their voltages.
• DC flows in one direction (cells and batteries). AC reverses direction periodically. India's mains supply is about 220–230 V at 50 Hz. AC is used for supply because its voltage can be changed easily with transformers.

Worked NDA-style MCQs

Q1. An electric iron of resistance 44 Ω is connected to a 220 V supply. The current is:
(a) 0.2 A (b) 5 A (c) 10 A (d) 9,680 A

I = V/R = 220/44 = 5 A. Answer: (b).

Q2. Resistors of 2 Ω, 3 Ω and 6 Ω are connected in parallel. The equivalent resistance is:
(a) 11 Ω (b) 2 Ω (c) 0.5 Ω (d) 1 Ω

1/R = 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 1, so R = 1 Ω, less than the smallest. In series it would be 11 Ω. Answer: (d).

Q3. A bulb is rated 60 W, 240 V. Its resistance and the current it draws at 240 V are:
(a) 960 Ω, 0.25 A (b) 4 Ω, 60 A (c) 240 Ω, 1 A (d) 480 Ω, 0.5 A

R = V²/P = 57,600/60 = 960 Ω. I = P/V = 60/240 = 0.25 A. Check: 240/960 = 0.25. Answer: (a).

Q4. A 1.5 kW geyser runs for 2 hours a day for 30 days. At ₹5 per unit, the cost is:
(a) ₹150 (b) ₹225 (c) ₹450 (d) ₹900

Energy = 1.5 × 2 × 30 = 90 kWh; cost = 90 × 5 = ₹450. Answer: (c).

Q5. A wire of resistance R is stretched uniformly to twice its length. Its new resistance is:
(a) R/2 (b) 2R (c) R (d) 4R

Length doubles and area halves, so R becomes 2 × 2 = 4 times. Answer: (d).

Q6. Bulbs rated 100 W and 60 W (both for 220 V) are connected in series across 220 V. Which glows brighter?
(a) 60 W (b) 100 W (c) both equally (d) neither glows

In series the current is common, so the higher resistance (the 60 W bulb) dissipates more power. Answer: (a).

Common mistakes

• Connecting a voltmeter in series or an ammeter in parallel.
• Adding resistances in parallel. Add reciprocals; the answer must be smaller than the smallest resistor.
• Assuming the higher-wattage bulb always glows brighter. Only in parallel.
• Thinking a fuse goes in the neutral wire. It goes in the live wire.
• Doubling resistance when a wire is stretched to double length. It becomes four times.

Practice set

1. A fuse wire should have: (a) high resistance and high melting point (b) zero resistance (c) high melting point only (d) low melting point
2. A current of 0.5 A flows for 10 minutes. The charge that passes is: (a) 5 C (b) 50 C (c) 300 C (d) 3,000 C
3. Resistors of 4 Ω and 12 Ω in parallel give: (a) 16 Ω (b) 8 Ω (c) 3 Ω (d) 0.33 Ω
4. A heater is rated 1,000 W, 200 V. Its resistance is: (a) 5 Ω (b) 0.2 Ω (c) 200 Ω (d) 40 Ω
5. When a metal wire is heated, its resistance: (a) increases (b) decreases (c) stays the same (d) becomes zero
6. A voltmeter is connected in a circuit: (a) in series (b) in parallel (c) either way (d) only with a fuse
7. A car battery is an example of: (a) a primary cell (b) a secondary cell (c) a dry cell (d) a solar cell
8. The filament of an incandescent bulb is made of: (a) tungsten (b) copper (c) nichrome (d) tin–lead alloy

Answers:

1. (d). It must melt quickly when the current is too high.
2. (c). Q = It = 0.5 × 600.
3. (c). 4 × 12/(4 + 12) = 48/16.
4. (d). R = V²/P = 40,000/1,000.
5. (a). The reverse is true for semiconductors.
6. (b). It measures the potential difference across a component.
7. (b). A rechargeable lead–acid battery.
8. (a). Its melting point is very high.

What to do next

• Memorise P = VI = I²R = V²/R and practise getting R and I from any rating.
• Solve 20 circuit problems mixing series, parallel and power, checking that every parallel answer is smaller than the smallest resistor.
• Work out your own home's monthly units from the appliances' wattage and hours of use.
• Continue to magnetism and electromagnetism, and use the physics revision sheet before mocks.