Chapter 7 · In-text questionsTextbook pages 131–153

In-text Questions – Solutions ധാരാവൈദ്യുതി

Every question asked inside the chapter, in the order of the book: the science-fair LED, charges and the capacitor, the water, heat and air analogies (Table 7.1), Fig 7.8, sources of emf (Table 7.2), the voltaic cell, Tables 7.3 and 7.4, the cell numericals, current numericals, circuit diagrams (Tables 7.5, 7.6), Ohm's law (Tables 7.7, 7.8, Graph 7.1), the factors of resistance (Table 7.9), the rheostat, series and parallel resistors (Fig 7.28–7.33), house wiring and AC/DC. Numericals are in exam layout: Given → Formula → Substitution → Answer.

📖 What you need (pages 5–10 of this guide)

1 · The science-fair LED (p131)

Textbook p131, opening picture

LED പ്രകാശിക്കുവാൻ എന്തിനായിരിക്കും ഈ ഘടകം സെർക്കീട്ടിൽ ഉൾപ്പെടുത്തിയത്? Why has this component been included in the circuit for lighting the LED? (At the school science fair ശാസ്ത്രോത്സവം, an LED was lit with a 9 V battery; a small striped component was joined next to it.)

The striped component is a resistor പ്രതിരോധകം. An LED needs only about 3 V. What would happen if the full 9 V were put across it? The book answers this on p153 – see section 36.

🔌 The circuit on the table, as a diagram
The component is a resistor, connected in series with the LED. It limits the current: part of the battery's p.d. is across the resistor, so the LED gets only the small p.d. (and current) it needs. Without it the LED would get too much current and burn out (the same idea as Fig 7.33 – section 36).

2 · Charges by rubbing (p131)

Textbook p131
🎬 Rubbing moves electrons
• Two kinds: positive പോസിറ്റീവ് and negative നെഗറ്റീവ് charge. The object that loses electrons becomes positive, the one that gains them becomes negative.
• The charge of an electron is negative.
• The SI unit of charge is the coulomb (C) കൂളോം.

3 · The capacitor and the button cell (Fig 7.1, 7.2)

Textbook pp131–132

ചാർജ് ചെയ്യപ്പെട്ട ഒരു കപ്പാസിറ്റർ (6 V, 500 µF) LED യുമായി ചിത്രം 7.1 ൽ കാണുന്നതുപോലെ ബന്ധിപ്പിക്കുക. Connect a charged capacitor കപ്പാസിറ്റർ (6 V, 500 µF) to an LED as in Fig 7.1.

A capacitor stores a fixed amount of charge; a cell keeps producing a potential difference from its chemicals.

🧪 Connect the LED – capacitor or button cell?

Illustration: the capacitor's LED fades within a few seconds (the exact time depends on the capacitor and the LED); the button cell keeps the LED lit for many hours.

• Observation: the LED glows for a very short time and then fades out.
• The capacitor's charge flows through the LED – the capacitor discharges.
• It does not glow continuously because the capacitor's stored charge is used up quickly; nothing keeps up the potential difference between its terminals.
• With the button cell (Fig 7.2) the LED glows continuously – the cell keeps a potential difference between its terminals, so charge flows all the time. The flow of charges through a circuit is an electric current.

4 · Two pots of water (Fig 7.3, 7.4)

Textbook p132
🎬 Same level, then A raised
• Fig 7.3: No – water does not flow.
• The gravitational potentials are equal (തുല്യമാണ്) – the levels are the same.
• Fig 7.4: Yes – now water flows from A to B, because there is a difference in the height of the levels.

5 · Heat, air and Table 7.1 (Fig 7.5, 7.6)

Textbook p133
🎬 Every flow goes from “more” to “less”
• The temperature rises first at Q (the end in the flame). • Heat flows from Q to P. • The pressure is higher inside the tube. • Air flows from inside the tube to outside.
Situation സന്ദർഭംDirection of flow പ്രവാഹദിശ
water flowingfrom the higher level to the lower level
heat flowingfrom the part at higher temperature to the part at lower temperature (given)
air flowingfrom the region of higher pressure to the region of lower pressure

6 · The pump of Fig 7.7 – and the flow of charges

Textbook p134

പാത്രം A യിൽ നിന്ന് പാത്രം B യിലേക്ക് ജലം തുടർച്ചയായി പ്രവഹിക്കുകയില്ലേ? എന്തായിരിക്കും കാരണം? If a pump returns from B to A, every second, as much water as flows from A to B, won't water flow from A to B continuously? What could be the reason?

ഒരു സെർക്കീട്ടിലൂടെ വൈദ്യുതചാർജുകളുടെ പ്രവാഹം സാധ്യമാകുന്നത് എങ്ങനെയാണ്? How is a (continuous) flow of electric charges through a circuit possible?

🎬 Pump ↔ cell
• Yes, the flow is continuous. The pump, an external energy source, keeps the difference in the water levels of A and B, so water keeps flowing.
• In the same way, a continuous flow of charge needs a source (a cell, battery or generator) that keeps a potential difference between two points of the circuit. Such a source is called a source of electricity വൈദ്യുതസ്രോതസ്സ്.

7 · Fig 7.8 – a bulb with no source

Textbook p134
🎬 Fig 7.8 redrawn – then with a cell between C and D
• No, the bulb will not glow.
• There is no source between C and D to maintain a potential difference, so no charges flow. A source of electricity joined between C and D would keep a p.d. and the bulb would glow.

8 · Sources of emf and Table 7.2

Textbook p135

emf ന്റെ ഒരു സ്രോതസ്സാണ് നമ്മൾ സാധാരണ ഉപയോഗിക്കുന്ന ടോർച്ച് സെൽ. നിങ്ങൾക്കറിയാവുന്ന emf ന്റെ മറ്റു സ്രോതസ്സുകൾ എഴുതി നോക്കൂ. ഇവ ഓരോന്നിലും നടക്കുന്ന ഊർജമാറ്റം സയൻസ് ഡയറിയിൽ എഴുതൂ. The torch cell we commonly use is a source of emf. Write other sources of emf you know (button cell, …) and the energy change in each, and complete Table 7.2.

🃏 What energy goes in? Tap one

Score: 0 / 0

Source of emf emf ന്റെ സ്രോതസ്സ്Energy change ഊർജമാറ്റം
torch cell (dry cell)chemical energy → electrical energy (given)
generatormechanical energy → electrical energy (given)
button cellchemical energy → electrical energy
solar celllight energy → electrical energy
car battery / storage cellchemical → electrical (electrical → chemical while charging)
bicycle dynamomechanical energy → electrical energy

9 · The voltaic cell; primary and secondary cells (Fig 7.9–7.11)

Textbook pp136–137
🧪 Voltaic cell – choose the metal, let it run

Approx. values: Cu–Zn about 1.1 V, Cu–Mg about 2.7 V (enough for an LED). The fall in brightness is an illustration – the real rate depends on the acid and the rods.

• The voltmeter needle deflects (about 1 V): electrons released by zinc's reaction with the acid flow through the outer circuit. Copper is at the higher potential (+), zinc at the lower (−); the current in the outer circuit flows from copper to zinc.
• The LED's brightness decreases after a while.
• Reason: the rate of the chemical reaction falls, so the electrical energy obtained also falls.
• Primary cells (can't be reused): dry cell, button cell, zinc–carbon and alkaline torch cells (AA, AAA, C).
• Secondary (storage) cells/batteries (rechargeable): mobile phone battery, inverter battery, car and two-wheeler batteries, laptop battery, power bank, emergency lamp battery.
⚠ Dilute sulphuric acid burns skin and eyes – do the voltaic-cell activity only in the school lab with your teacher, wearing goggles.

10 · Connecting a voltmeter (Fig 7.12) and Table 7.3

Textbook p137
🔌 Fig 7.12 as a diagram
• The voltmeter's + terminal → the cell's + terminal; its − terminal → the cell's − terminal.
Source സ്രോതസ്സുകൾPotential difference (V) – typical, approx.
torch cell (dry cell)1.5 V
button cell3 V (CR2032 lithium; some button cells 1.5 V)
voltaic cell≈ 1.1 V
mobile battery3.7 V
Sample readings – your real readings will differ.

11 · Combining two torch cells (Fig 7.13, Table 7.4)

Textbook p138

രണ്ട് ടോർച്ച് സെല്ലുകൾ ചിത്രത്തിൽ കാണുന്നതുപോലെ മൂന്ന് വ്യത്യസ്ത രീതിയിൽ ക്രമീകരിച്ച് അവയിൽ ഓരോന്നിലും ലഭിക്കുന്ന പൊട്ടെൻഷ്യൽ വ്യത്യാസം വോൾട്ട്മീറ്റർ ഉപയോഗിച്ച് അളന്ന് പട്ടികപ്പെടുത്തുക. Arrange two torch cells in the three ways shown (Fig 7.13 (a), (b), (c)), measure the p.d. in each with a voltmeter and complete Table 7.4.

🎬 The three arrangements with the voltmeter
CircuitNumber of cellsVoltmeter reading / p.d. (V)
1 – Fig 7.13 (a), series23 V
2 – Fig 7.13 (b), parallel21.5 V
3 – Fig 7.13 (c), + joined to +20 V
• The greatest p.d. is in the series arrangement ശ്രേണീരീതി (+ of one cell to − of the next): the emfs add.
• Series examples: TV remote control, torch with 2–3 cells in a line, toy cars, calculators, wall clock with two cells, the 4.5 V pack of Fig 7.15.
• Never arrange cells as in Fig 7.13 (c) – they oppose each other and give no p.d.

12 · Four 1.5 V cells – the greatest p.d.

Textbook p139 · ❓ question

നിങ്ങൾക്ക് 1.5 V emf വീതം ഉള്ള നാല് സെല്ലുകൾ തന്നിരിക്കുന്നു. ഇവ ഉപയോഗിച്ചുണ്ടാക്കാവുന്ന പരമാവധി പൊട്ടെൻഷ്യൽ വ്യത്യാസം എത്ര? ഇതിന്റെ ക്രമീകരണ രീതി ചിത്രീകരിക്കുക. You are given four cells of emf 1.5 V each. What is the maximum potential difference you can get from them? Draw the arrangement.

Which arrangement adds the emfs? Join + of one cell to − of the next.

🎬 Solution in exam layout
Given: 4 cells, emf 1.5 V each. Formula: in series, total emf = sum of the emfs. Substitution: 1.5 + 1.5 + 1.5 + 1.5 = 4 × 1.5. Answer: 6 V, with all four cells in series (− + − + − + − +).

13 · A 9 V battery of six cells

Textbook p139 · ❓ question

9 V ന്റെ ബാറ്ററിയിൽ സമാനമായ 6 സെല്ലുകൾ ശ്രേണീരീതിയിലാണ് ഘടിപ്പിച്ചത് എങ്കിൽ ഒരു സെല്ലിന്റെ emf എത്ര ? If a 9 V battery is made of 6 identical cells connected in series, what is the emf of one cell?

In series the emfs add: 6 × (emf of one cell) = 9 V.

🎬 Solution in exam layout – inside a 9 V battery
Given: total emf = 9 V; 6 identical cells in series. Formula: total emf = n × (emf of one cell), so emf of one cell = total ÷ n. Substitution: 9 V ÷ 6. Answer: 1.5 V.
⚠ Never short-circuit a cell or battery; never put cells in your mouth; stop if a battery gets hot; keep water and fire away; dispose of batteries (nickel, cadmium, lead) at e-waste collection points.

14 · 10 C in 5 s

Textbook p140 · ❓ question

ഒരു ചാലകത്തിലൂടെ 10 C ചാർജ് ഒഴുകാൻ 5 s സമയം എടുത്തുവെങ്കിൽ കറന്റ് എത്ര ? If 10 C of charge takes 5 s to flow through a conductor, what is the current?

Current = charge flowing per second, I = Q/t.

🎬 Solution in exam layout – counting the charge
🧪 Try other numbers
Given: Q = 10 C; t = 5 s. Formula: I = Q/t. Substitution: I = 10 C ÷ 5 s. Answer: I = 2 A.

15 · 1.5 A for 3 s

Textbook p140 · ❓ question

ഒരു ചാലകത്തിലൂടെ 1.5 A കറന്റ് 3 s പ്രവഹിക്കുന്നുവെങ്കിൽ ചാലകത്തിലൂടെ ഒഴുകിയ വൈദ്യുതചാർജിന്റെ അളവ് കണക്കാക്കുക. If a current of 1.5 A flows through a conductor for 3 s, calculate the amount of charge that flowed.

Rearrange I = Q/t to get Q.

🎬 Solution in exam layout
Given: I = 1.5 A; t = 3 s. Formula: I = Q/t, so Q = I × t. Substitution: Q = 1.5 A × 3 s. Answer: Q = 4.5 C.
⚠️ Common trap

Dividing instead of multiplying (1.5 ÷ 3 = 0.5). Check the units: A = C/s, so A × s = C – multiplying gives coulombs.

16 · An ammeter reads 1 A

Textbook p141

ഒരു വൈദ്യുതസെർക്കീട്ടിൽ ബന്ധിപ്പിച്ചിരിക്കുന്ന അമ്മീറ്ററിൽ 1 A റീഡിങ് കാണിക്കുന്നു എങ്കിൽ 1 s കൊണ്ട് അമ്മീറ്ററിലൂടെ ഒഴുകിയ ചാർജ് എത്ര? An ammeter in a circuit reads 1 A. How much charge flowed through the ammeter in 1 s?

🎬 Solution in exam layout – Fig 7.18 as a diagram
Given: I = 1 A; t = 1 s. Formula: Q = I × t. Substitution: Q = 1 A × 1 s. Answer: Q = 1 C – that is what “1 ampere” means: 1 coulomb per second.

17 · Circuit diagrams – Fig 7.19 and Table 7.5

Textbook p142
🎬 Table 7.5 symbols, then a circuit built from them
A sample circuit: a battery of two cells, a switch, a bulb and an ammeter in series (the stepper above, last step). Three components and their uses:
• Battery ബാറ്ററി – source of electricity; keeps a potential difference so that current flows.
• Switch / key സ്വിച്ച് / കീ – closes (on) or breaks (off) the circuit.
• Bulb ബൾബ് – changes electrical energy into light (and heat).
(Also: ammeter – measures current, in series; voltmeter – measures p.d., in parallel; LED – gives light, current only one way.)

18 · Fig 7.21 and Table 7.6 – voltmeter and ammeter

Textbook pp142–143 · ❓ question

ചിത്രം 7.21 ൽ കാണിച്ച സെർക്കീട്ട് നിരീക്ഷിച്ച് അമ്മീറ്റർ, വോൾട്ട്മീറ്റർ എന്നിവയുടെ പ്രതീകം, ഉപയോഗം, സെർക്കീട്ടിൽ ഘടിപ്പിക്കുന്ന രീതി എന്നിവ പട്ടികപ്പെടുത്തുക. Observe the circuit of Fig 7.21 and tabulate the symbol, use and way of connecting the ammeter and the voltmeter (Table 7.6).

🔌 Fig 7.21 redrawn with the current direction
Voltmeter വോൾട്ട്മീറ്റർAmmeter അമ്മീറ്റർ
symbol—Ⓥ——Ⓐ— (given)
useto measure potential difference (given)to measure current
connectionin parallel with the component (given)in series in the circuit
terminals+ terminal to the side connected to the cell's +, − terminal to the side of the cell's −+ terminal towards the cell's +, − towards the cell's − (given)

19 · Ohm's activity – Table 7.7 (Fig 7.22)

Textbook pp143–144

രണ്ട് ടോർച്ച് സെല്ലുകൾ, അമ്മീറ്റർ, പ്രതിരോധകം, സ്വിച്ച് എന്നിവ ഉൾപ്പെടുത്തി (ചിത്രം 7.22) ഒരു സെർക്കീട്ട് നിർമ്മിക്കുക. … ശ്രേണീരീതിയിൽ സെല്ലുകളുടെ എണ്ണം വർധിപ്പിച്ച് പ്രവർത്തനം ആവർത്തിക്കുക. Build the circuit of Fig 7.22 (torch cells, ammeter, resistor, switch, voltmeter across the resistor). Measure the p.d. and the current, then repeat with more cells in series (Table 7.7).

🧪 Fig 7.22 – add cells and read the meters

Sample readings – your real readings will differ. Model: R = 10 Ω, 1.5 V per cell, ideal meters.

Number of cellsVoltage V (V)Current I (A)V/I
230.3010
34.50.4510
460.6010
• More cells → the voltmeter reading (p.d.) increases. • When the current increases, the p.d. also increases (in the same proportion). • Yes, V/I is almost constant: I ∝ V, so V = constant × I and V/I = a constant = the resistance R of the circuit. R = V/I.

20 · The unit of resistance; more resistance, less current

Textbook pp144–145
🧪 Same 3 V, change the resistance
• R = V/I, so unit of resistance = unit of p.d. ÷ unit of current = volt/ampere (V/A), named the ohm (Ω). 1 kΩ = 1000 Ω; 1 MΩ = 1000 kΩ.
• When the resistance increases (same p.d.), the current decreases (കുറയുന്നു) – I = V/R.
• SI unit of resistance: ohm (Ω).

21 · Table 7.8 and Graph 7.1

Textbook p145 · ❓ question

ഓം നിയമത്തിന്റെ അടിസ്ഥാനത്തിൽ പട്ടിക 7.8 പൂർത്തിയാക്കി ഒരു ഗ്രാഫ് വരയ്ക്കുക. വോൾട്ടേജ് Y അക്ഷത്തിലും കറന്റ് X അക്ഷത്തിലും രേഖപ്പെടുത്തുക. നിങ്ങൾക്ക് ലഭിച്ച ഗ്രാഫിന്റെ പ്രത്യേകത എന്ത്? Complete Table 7.8 using Ohm's law and draw a graph with voltage on the Y-axis and current on the X-axis. What is special about the graph you get?

VIR
9 V1 A?
3 V?6 Ω
?2 A3 Ω

Use the form of Ohm's law that has the missing quantity alone: R = V/I, I = V/R, V = IR.

🎬 Solution in exam layout – filling the table and plotting
Row 1: Given V = 9 V, I = 1 A; R = V/I = 9 ÷ 1 = 9 Ω.
Row 2: Given V = 3 V, R = 6 Ω; I = V/R = 3 ÷ 6 = 0.5 A.
Row 3: Given I = 2 A, R = 3 Ω; V = IR = 2 × 3 = 6 V.
Graph: for any one resistor the V–I graph is a straight line through the origin (V ∝ I) and its slope is R. The three rows are three different resistors, so each point lies on its own line through O – the steepest line is the largest resistance (9 Ω), the least steep the smallest (3 Ω).

22 · The heater coil, hot and cold

Textbook p146

വൈദ്യുത ഹീറ്ററിൽ ഉപയോഗിക്കുന്ന നിക്രോം കമ്പിയുടെ പ്രതിരോധം, ഹീറ്റർ ഓഫാക്കിയ ഉടനെയും തണുത്ത ശേഷവും മൾട്ടിമീറ്റർ ഉപയോഗിച്ച് അളക്കുക. Measure the resistance of the nichrome നിക്രോം wire of an electric heater with a multimeter just after switching it off and again after it cools.

🧪 Cooling coil on the multimeter

Illustration (unplugged heater element; numbers are only a sample): nichrome's resistance rises by roughly 5–10 % when it is red-hot.

• The resistance is greater when the coil is hot (just after switching off). As the temperature falls, the resistance decreases – resistance depends on temperature താപനില.
• Yes – other factors also affect resistance: the length, the thickness (area of cross-section) and the material (see the next activity).
⚠ Measure a heater's resistance only after it is unplugged from the mains – never touch a heater element while it is connected or still hot.

23 · Fig 7.25 and Table 7.9 – length, thickness, material

Textbook pp146–147

CD: nichrome wire 40 cm (M its midpoint); EF: nichrome, same length, double thickness; GH: copper, same length and thickness as CD. The free end J (joined to the battery's −) touches M, D, F, H in turn. Observe the bulb and the ammeter and complete Table 7.9.

🧪 Fig 7.25 – touch J to each point

Sample model – your real readings will differ: 3 V battery; bulb taken as a fixed 3 Ω; CD (40 cm thin nichrome) = 6 Ω; “double thickness” taken as double the area of cross-section, so EF = 3 Ω; copper GH ≈ 0.01 Ω; ideal ammeter.

J toucheslength / thicknessmaterialammeter reading (sample)
M20 cmnichrome0.5 A – larger, brighter
D40 cmnichrome0.33 A – least
F40 cm, thickernichrome0.5 A – more than D
H40 cmcopper≈ 1 A – largest
• Least current: at D. • Reason: largest resistance (പ്രതിരോധം കൂടുതൽ) – the battery's p.d. is the same each time, and V = IR. • Longer conductor → resistance increases. • Thicker conductor → resistance decreases. • Same length and thickness: nichrome has more resistance than copper.

24 · Factors of resistance and the rheostat (Fig 7.26, 7.27)

Textbook p148
🧪 Fig 7.26/7.27 – slide the contact S

Model: 3 V battery, bulb taken as a fixed 3 Ω, rheostat of 100 turns × 0.15 Ω (the rheostat of the next question).

• Factors: the nature of the material; the thickness (area of cross-section); the length (and the temperature). Longer → more resistance; thicker → less; nichrome and tungsten high, aluminium and copper very low, silver the lowest.
• Principle of the rheostat: for a conductor of the same thickness, resistance increases with its length. Moving the sliding contact S changes the length (the number of turns) of the resistance wire in the circuit, so the resistance – and the current – change as needed.

25 · A rheostat of 100 turns, 0.15 Ω each

Textbook p149 · ❓ question

ഒരു റിയോസ്റ്റാറ്റിൽ പ്രതിരോധ കമ്പിയുടെ 100 ചുറ്റുകളാണ് ഉള്ളത്. ഒരു ചുറ്റിന്റെ പ്രതിരോധം 0.15 Ω ആണ്, എങ്കിൽ ഈ റിയോസ്റ്റാറ്റ് ഉപയോഗിച്ച് ഒരു സെർക്കീട്ടിൽ ഉൾപ്പെടുത്താൻ കഴിയാത്ത പ്രതിരോധത്തിന്റെ മൂല്യം താഴെ കൊടുത്തവയിൽ ഏതാണ്? നിങ്ങളുടെ ഉത്തരം സാധൂകരിക്കുക. A rheostat has 100 turns of resistance wire; each turn has a resistance of 0.15 Ω. Which of these values of resistance can NOT be included in a circuit using this rheostat? Justify your answer.

a) 3 Ωb) 7.5 Ωc) 4 Ωd) 8.25 Ω

The sliding contact can only include a whole number of turns. Divide each value by 0.15 Ω.

🎬 Solution – count the turns for each value
Given: 100 turns, 0.15 Ω per turn (maximum 15 Ω). Formula: number of turns = R ÷ 0.15 Ω – it must be a whole number.
Substitution: 3 ÷ 0.15 = 20 ✔; 7.5 ÷ 0.15 = 50 ✔; 4 ÷ 0.15 = 26.67 ✘; 8.25 ÷ 0.15 = 55 ✔.
Answer: (c) 4 Ω – it would need 26.67 turns, and part of a turn cannot be selected.

26 · Fig 7.28 – bulbs in series and in parallel

Textbook pp149–150

3 V ബാറ്ററി, സ്വിച്ചുകൾ, 3 V ബൾബുകൾ എന്നിവ ഉപയോഗിച്ച് താഴെക്കൊടുത്ത രീതിയിൽ (ചിത്രം 7.28 (a), (b)) രണ്ട് സെർക്കീട്ടുകൾ നിർമ്മിക്കുക. Build the two circuits of Fig 7.28 with a 3 V battery, switches and 3 V bulbs (3 W, 3 V).

🧪 Fig 7.28 – work the switches

Model: each 3 W, 3 V bulb is taken as a fixed resistance of 3 Ω (R = V²/P – a “go further” formula); ideal 3 V battery.

• Both switches on: the bulbs of (b), the parallel circuit, glow more brightly.
• Only S₁ on: in (a) neither bulb glows – the single series path is broken at S₂; in (b) only the bulb with S₁ glows – it has its own path.
• In (b) each bulb gets the battery's full 3 V (and more current, 1 A); in (a) the two bulbs share the 3 V – 1.5 V each, 0.5 A. A larger p.d. and current give a brighter glow.

27 · p.d. across resistors in series

Textbook p151
🧪 Share the p.d. – two resistors in series on 6 V
• The same current I flows through both, and V = IR – so the resistor with the higher resistance has more (കൂടുതൽ) p.d. across it.
• Equal resistors in series have equal (തുല്യം) p.d. across them.

28 · 8 Ω and 4 Ω with a 6 V battery, in series

Textbook p151 · ❓ question

8 Ω, 4 Ω എന്നീ രണ്ട് പ്രതിരോധകങ്ങളും 6 V ബാറ്ററിയും തന്നിരിക്കുന്നു. a) ഇവയെ ശ്രേണീരീതിയിൽ ബന്ധിപ്പിക്കുന്നതിന്റെ സെർക്കീട്ട് ഡയഗ്രം വരയ്ക്കുക. b) സെർക്കീട്ടിലെ സഫലപ്രതിരോധം കണ്ടുപിടിക്കുക. c) സെർക്കീട്ടിലൂടെയുള്ള കറന്റ് എത്രയെന്ന് കണക്കാക്കുക. Two resistors of 8 Ω and 4 Ω and a 6 V battery are given. (a) Draw the circuit diagram connecting them in series. (b) Find the effective resistance സഫലപ്രതിരോധം. (c) Calculate the current in the circuit.

Series: R = R₁ + R₂, then I = V/R.

🎬 Solution in exam layout
(a) Diagram: battery, switch, 8 Ω and 4 Ω one after the other in a single loop (above).
Given: R₁ = 8 Ω, R₂ = 4 Ω, V = 6 V. (b) Formula R = R₁ + R₂; substitution 8 + 4; answer R = 12 Ω.
(c) Formula I = V/R; substitution 6 V ÷ 12 Ω; answer I = 0.5 A. (Extra: V across 8 Ω = 0.5 × 8 = 4 V; across 4 Ω = 2 V; 4 + 2 = 6 V.)

29 · Ten 2 Ω resistors in series

Textbook p151 · ❓ question

2 Ω വീതം പ്രതിരോധമുള്ള പത്ത് പ്രതിരോധകങ്ങൾ ശ്രേണീരീതിയിൽ ബന്ധിപ്പിച്ചാൽ ലഭിക്കുന്ന സഫലപ്രതിരോധം എത്ര? What effective resistance do you get by connecting ten resistors of 2 Ω each in series?

🎬 Solution in exam layout
Given: n = 10, R = 2 Ω each, in series. Formula: effective resistance = nR. Substitution: 10 × 2 Ω. Answer: 20 Ω.

30 · How many 6 Ω resistors make 42 Ω?

Textbook p151 · ❓ question

6 Ω പ്രതിരോധമുള്ള എത്ര പ്രതിരോധകങ്ങൾ ശ്രേണീരീതിയിൽ ബന്ധിപ്പിച്ചാലാണ് 42 Ω സഫലപ്രതിരോധം ലഭിക്കുക? How many 6 Ω resistors must be connected in series to get an effective resistance of 42 Ω?

🎬 Solution in exam layout
Given: R = 6 Ω each; total 42 Ω in series. Formula: total = nR, so n = total ÷ R. Substitution: n = 42 Ω ÷ 6 Ω. Answer: 7 resistors.

31 · 6 Ω and 3 Ω with a 6 V battery, in parallel

Textbook p152 · ❓ question

6 Ω, 3 Ω എന്നീ രണ്ട് പ്രതിരോധകങ്ങളും 6 V ബാറ്ററിയും തന്നിരിക്കുന്നു. a) ഇവയെ സമാന്തരമായി ബന്ധിപ്പിക്കുന്നതിന്റെ സെർക്കീട്ട് ഡയഗ്രം വരയ്ക്കുക. b) സെർക്കീട്ടിലെ സഫലപ്രതിരോധം കണ്ടുപിടിക്കുക. c) ഓരോ പ്രതിരോധകത്തിലൂടെയുമുള്ള കറന്റ് എത്രയെന്ന് കണക്കാക്കുക. Two resistors of 6 Ω and 3 Ω and a 6 V battery are given. (a) Draw the circuit diagram connecting them in parallel. (b) Find the effective resistance. (c) Calculate the current through each resistor.

Parallel: R = R₁R₂/(R₁ + R₂). Each resistor gets the full 6 V, so the current in each is 6 V ÷ its own R.

🎬 Solution in exam layout
(a) Diagram: the 6 Ω and 3 Ω side by side between the same two points, joined across the battery (above).
Given: R₁ = 6 Ω, R₂ = 3 Ω, V = 6 V. (b) Formula R = R₁R₂/(R₁ + R₂); substitution (6 × 3)/(6 + 3) = 18/9; answer R = 2 Ω.
(c) Formula I = V/R for each; substitution 6 V ÷ 6 Ω and 6 V ÷ 3 Ω; answer I₁ = 1 A, I₂ = 2 A (total 3 A = 6 V ÷ 2 Ω ✓).
⚠️ Common trap

Adding the resistances (6 + 3 = 9 Ω) – that is the series rule. In parallel the effective resistance is always less than the smallest resistor: 2 Ω < 3 Ω.

32 · Equal resistors in parallel

Textbook p152 · ❓ question

ഒരേ മൂല്യമുള്ള പ്രതിരോധകങ്ങളാണ് സമാന്തര രീതിയിൽ ഘടിപ്പിക്കുന്നതെങ്കിൽ ഓരോ പ്രതിരോധകത്തിലൂടെയുമുള്ള കറന്റ് എപ്രകാരമായിരിക്കും? If equal resistors are connected in parallel, how will the current through each resistor be?

🔌 Three equal 6 Ω resistors in parallel on 6 V
The current through each is equal. Each resistor has the same p.d. across it (parallel) and the same resistance, so I = V/R is the same for each; the total current divides equally (for n equal resistors, each carries I ÷ n).

33 · Five 10 Ω resistors in parallel

Textbook p152 · ❓ question

10 Ω വീതം പ്രതിരോധമുള്ള അഞ്ച് പ്രതിരോധകങ്ങൾ സമാന്തരമായി ഘടിപ്പിച്ചാൽ ലഭിക്കുന്ന സഫലപ്രതിരോധം എത്ര? What is the effective resistance when five resistors of 10 Ω each are connected in parallel?

🎬 Solution in exam layout
Given: n = 5, R = 10 Ω each, in parallel. Formula: effective resistance = R/n (from 1/R = 1/10 + 1/10 + 1/10 + 1/10 + 1/10 = 5/10). Substitution: 10 Ω ÷ 5. Answer: 2 Ω.

34 · Fig 7.32 – 2 Ω with two 2 Ω in parallel

Textbook p152 · ❓ question

ചിത്രം 7.32 ൽ കൊടുത്ത ക്രമീകരണത്തിന്റെ സഫലപ്രതിരോധം എത്രയെന്ന് കണ്ടുപിടിക്കുക. Find the effective resistance of the arrangement in Fig 7.32.

First replace the two parallel 2 Ω resistors by one resistor; then it is in series with the first 2 Ω.

🎬 Solution in exam layout – Fig 7.32 redrawn
Given: 2 Ω in series with (2 Ω ∥ 2 Ω). Formula: parallel R = R₁R₂/(R₁ + R₂); then series R = R₁ + R₂. Substitution: (2 × 2)/(2 + 2) = 1 Ω; then 2 Ω + 1 Ω. Answer: 3 Ω.

35 · Series and parallel – differences; house wiring

Textbook pp152–153
🔌 A house circuit – every appliance across the same two mains wires
SeriesParallel
the same current through every resistorthe same p.d. across every resistor
the p.d. is divided (more across the larger R)the current is divided (more through the smaller R)
effective R increases: R = R₁ + R₂effective R decreases: 1/R = 1/R₁ + 1/R₂ (less than the smallest)
one break stops the whole circuitthe other branches keep working
used in decoration serial lights, a fuse, a regulatorused for household appliances
• Household appliances are connected in parallel.
• Advantages: each appliance gets the full 230 V; each can be switched on and off independently; if one fails or is switched off, the others keep working.
⚠ Never experiment with the mains supply (230 V AC) at home – it can kill. Use only torch cells or a 9 V battery.

36 · Fig 7.33 – protecting a 3 V bulb on 9 V

Textbook p153

3 V പൊട്ടെൻഷ്യൽ വ്യത്യാസത്തിൽ പ്രവർത്തിക്കുന്ന ബൾബ്, 12 Ω പ്രതിരോധകം, 9 V ബാറ്ററി എന്നിവ ഉൾപ്പെടുന്ന ഒരു സെർക്കീട്ടും [ചിത്രം 7.33 (a)] 12 Ω പ്രതിരോധകം ഉൾപ്പെടാത്ത മറ്റൊരു സെർക്കീട്ടുമാണ് [ചിത്രം 7.33 (b)] നൽകിയിരിക്കുന്നത്. ബൾബിന്റെ പ്രതിരോധം 6 Ω ആണ്. Fig 7.33 (a): a bulb that works at 3 V, a 12 Ω resistor and a 9 V battery; Fig 7.33 (b): the same without the 12 Ω resistor. The bulb's resistance is 6 Ω.

Find the total resistance and the current in each circuit, then V = IR for the bulb alone.

🎬 Solution in exam layout – Fig 7.33 (a) and (b)
Given: bulb 6 Ω (works at 3 V); resistor 12 Ω; battery 9 V.
• More resistance: (a) – R = 6 + 12 = 18 Ω, against 6 Ω in (b).
• (a): I = V/R = 9 V ÷ 18 Ω = 0.5 A; V(bulb) = IR = 0.5 A × 6 Ω = 3 V – so the bulb gets 3 V in (a) (the resistor takes the other 6 V).
• (b): the bulb gets the whole 9 V; I = 9 ÷ 6 = 1.5 A – three times the 0.5 A it is made for. Too much current: the bulb fuses (burns out).
This is why the science-fair LED had a resistor in series – to limit the current (section 1).

37 · Battery electricity and house electricity – DC and AC

Textbook p153

ബാറ്ററി/സെല്ല് എന്നിവയിൽ നിന്ന് ലഭിക്കുന്ന വൈദ്യുതിയും നമ്മുടെ വീടുകളിൽ ലഭിക്കുന്ന വൈദ്യുതിയും തമ്മിൽ എന്തെങ്കിലും വ്യത്യാസമുണ്ടോ? Is there any difference between the electricity from a battery or cell and the electricity we get at home?

📈 Current against time
Yes. A battery gives current in one direction only – direct current (DC), at a low p.d. (1.5 V, 9 V, 12 V…). The electricity at home changes direction at regular intervals – alternating current (AC) – and is at a high voltage, 230 V. So the experiments of this chapter must never be done with household electricity. Discuss with elders the precautions to take when handling it.
⚠ Never experiment with the mains supply (230 V AC) at home – it can kill. Use only torch cells or a 9 V battery. Never touch switches with wet hands, and keep away from fallen or sagging power lines in the monsoon – call KSEB.

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