Vardaan Watermark

Vardaan Learning Institute

Created by Team Vardaan with ♥
LIGHT & CURRENT ELECTRICITY — HIGH-LEVEL PRACTICE SET 1Time: 3 Hours
Class: 10  |  CBSE Board Pattern  |  Emphasis on Numericals90 Questions
Attempt all questions. Show step-by-step working for all numerical problems using proper sign convention. Draw neat, labelled diagrams where required. For MCQs, choose the single best option.  |  Solutions: Light and Current Practice1Solution.html

☀ Section 1 — Light: Reflection, Refraction, Human Eye & Atmospheric Phenomena

Q1–Q45  |  MCQ (Q1–Q15) • Numericals & Short Answer (Q16–Q35) • Long Answer (Q36–Q45)
  1. A concave mirror has focal length 15 cm. An object is placed 10 cm from it. Which of the following correctly describes the image? MCQ
    • Real, inverted, magnified, in front of mirror
    • Virtual, erect, magnified, behind mirror
    • Real, inverted, at infinity
    • Virtual, erect, diminished, behind mirror
  2. A convex lens of focal length 20 cm is placed coaxially with a concave lens of focal length 30 cm. They are separated by 10 cm. An object is placed 60 cm in front of the convex lens. The final image is formed: MCQ
    • 40 cm beyond concave lens (real)
    • 30 cm in front of concave lens (virtual)
    • 20 cm beyond concave lens (real)
    • At infinity
  3. A ray of light enters a glass slab (n = 1.5) at an angle of 60°. After passing through a slab of thickness 4.8 cm, it exits the other side. The lateral shift d of the emergent ray is closest to: MCQ
    • 1.2 cm
    • 2.0 cm
    • 1.6 cm
    • 2.4 cm
  4. A person with myopia has far point 80 cm. A person with hypermetropia has near point 1 m. If both defects are in the SAME eye, the net power of the combined corrective lens to see distant objects is: MCQ
    • −1.25 D
    • +1.25 D
    • −2.25 D
    • +2.25 D
  5. The graph below shows V-I characteristics for three optical media. A ray passes from medium with the smallest critical angle to air. Which medium is it? MCQ
    • Medium with highest refractive index
    • Medium with lowest refractive index
    • Medium with refractive index = 1
    • All have same critical angle
  6. A student focuses a distant tree on a white screen using a convex lens. She then covers the upper half of the lens with black paper. The image formed on the screen will be: MCQ
    • Only the lower half of the tree
    • Full image of tree, but dimmer
    • Full image, same brightness
    • Only the upper half of the tree
  7. A ray of light traveling in air hits a flat glass surface at 45°. If nᴳₗₐ⸡⸡ = 1.5, which of the following quantities does NOT change as it enters glass? MCQ
    • Wavelength
    • Speed
    • Frequency
    • Direction
  8. An object is placed at the centre of curvature C of a concave mirror. The image is: MCQ
    • At C itself, real, inverted, same size
    • At F, real, inverted, diminished
    • Behind mirror, virtual, erect, magnified
    • At infinity
  9. A biconcave lens of focal length f is immersed in a liquid of same refractive index as the lens material. In the liquid, the lens acts as a: MCQ
    • Converging lens with same focal length f
    • Diverging lens with same focal length f
    • Plane glass with no converging or diverging effect
    • Converging lens with focal length 2f
  10. Assertion (A): The sky near the horizon appears lighter (whitish) than the sky overhead which is deep blue.
    Reason (R): Near the horizon, light has to travel through more atmosphere so all wavelengths are scattered. A&R
    A: The sky near the horizon appears whitish, not deep blue.
    R: Light passing through more atmosphere near the horizon undergoes multiple scattering events, mixing all wavelengths to give a whitish appearance.
    1. Both A and R are true, and R is the correct explanation of A.
    2. Both A and R are true, but R is NOT the correct explanation.
    3. A is true but R is false.
    4. A is false but R is true.
  11. Assertion (A): When a beam of white light falls on a glass prism, the violet colour deviates the most.
    Reason (R): Violet has the shortest wavelength among visible colours, so it has the highest refractive index in glass. A&R
    A: Violet light deviates most when white light passes through a glass prism.
    R: Violet has the shortest wavelength and the refractive index of glass for violet is highest, causing maximum deviation.
    1. Both A and R are true, and R is the correct explanation of A.
    2. Both A and R are true, but R is NOT the correct explanation.
    3. A is true but R is false.
    4. A is false but R is true.
  12. Assertion (A): Stars twinkle but planets do not.
    Reason (R): Stars, being point sources, show twinkling due to atmospheric refraction; planets are extended sources so net twinkling averages out. A&R
    A: Stars twinkle but planets do not twinkle noticeably.
    R: Stars are so far that they appear as point sources. Planets appear as extended sources (small discs), so random refractive shifts average to zero.
    1. Both A and R are true, and R is the correct explanation of A.
    2. Both A and R are true, but R is NOT the correct explanation.
    3. A is true but R is false.
    4. A is false but R is true.
  13. An object is placed 30 cm from a convex lens of focal length 20 cm. If the lens is replaced by a concave lens of focal length 60 cm, the image distance changes from: MCQ
    • +60 cm to −17.1 cm
    • −60 cm to +17.1 cm
    • +60 cm to +17.1 cm
    • −60 cm to −17.1 cm
  14. A person can read clearly only from 25 cm to 200 cm. She is: MCQ
    • Only myopic
    • Only hypermetropic
    • Both myopic and hypermetropic (presbyopic)
    • Normal vision
  15. Light of wavelength 600 nm in air enters glass of refractive index 1.5. Its wavelength inside glass is: MCQ
    • 900 nm
    • 400 nm
    • 600 nm
    • 360 nm
  16. An object of height 6 cm is placed 25 cm from a concave mirror of focal length 10 cm. Using the mirror formula: Numerical
    1. Find the image distance.
    2. Find the image height (magnification).
    3. State the nature and position of the image.
  17. A convex mirror used as a rear-view mirror has a radius of curvature 3.6 m. A truck 4.5 m wide is 5 m behind the mirror. Numerical
    1. Find the image distance of the truck.
    2. Find the width of the truck's image.
    3. What is the angular field of view advantage of convex over plane mirrors?
  18. A concave mirror has radius of curvature 40 cm. An object 3 cm tall is placed at (i) 30 cm, (ii) 20 cm, and (iii) 10 cm from the mirror. For each position: find image distance, image height, and nature of image. Numerical
  19. A convex lens of focal length 15 cm forms a real image 45 cm from the lens. Numerical
    1. Find the object distance.
    2. Find the magnification produced.
    3. If the object is 2 cm tall, find the height of the image.
  20. An object 4 cm high is placed 6 cm in front of a concave lens of focal length 12 cm. Numerical
    1. Find the image distance using the lens formula.
    2. Find the height of the image.
    3. State whether the image is real or virtual, erect or inverted.
  21. A convex lens (f = 20 cm) and a concave lens (f = 40 cm) are placed in contact with each other. Numerical
    1. Find the power and focal length of the combination.
    2. An object is placed 60 cm from the combination. Find the image distance.
    3. Is the image real or virtual?
  22. A ray of light travels from glass (n = 1.5) to water (n = 1.33). Find: Numerical
    1. The critical angle for total internal reflection at the glass-water interface.
    2. The angle of refraction if the angle of incidence is 30°. (sin 30° = 0.5)
    3. What happens if the angle of incidence is beyond the critical angle?
  23. The refractive index of glass is 1.5 and that of water is 1.33. If the speed of light in vacuum is $3 \times 10^8$ m/s, find: Numerical
    1. Speed of light in glass.
    2. Speed of light in water.
    3. Refractive index of glass with respect to water.
  24. A person with myopia cannot see objects clearly beyond 1.5 m. Numerical
    1. Find the power and focal length of the corrective lens.
    2. Draw a ray diagram showing: (a) the defective myopic eye and (b) the corrected eye with lens.
  25. A hypermetropic person has a near point of 60 cm. Find the power and focal length of the corrective lens that allows him to read clearly at 25 cm. Also verify by finding the image position using the lens formula. Numerical
  26. An object is placed at 2f from a convex lens of focal length f = 12 cm. Numerical
    1. Find image position using lens formula.
    2. Find magnification.
    3. If object is now moved to a distance of 1.5f, where does the image form?
  27. A glass slab (n = 1.6) of thickness 6 cm is placed in air. A ray strikes one face at 50° angle of incidence. Numerical
    1. Find angle of refraction inside glass. (sin 50° = 0.766, sin¹(0.479) ≈ 28.6°)
    2. Find lateral displacement of the emergent ray. [d = t × sin(i−r)/cos r]
    3. What is the angle between incident and emergent ray?
  28. A combination of two lenses: Lens A (f = +10 cm) and Lens B (f = −30 cm) placed in contact. An object is placed 15 cm from this combination. Numerical
    1. Find the focal length of the combination.
    2. Find image distance using the combination's focal length.
    3. Find magnification of the combination.
  29. The far point of a myopic student is 40 cm. He uses a concave lens to correct his vision. With the corrective lens, he can see an object at infinity. Numerical
    1. Find the power of the lens used.
    2. If the lens is now used as a magnifying glass (object placed at focal point), what is the magnification?
    3. Where should an object be placed to form an erect, virtual image at 40 cm?
  30. A student uses a convex lens as a projector. The object (slide) is placed 6 cm from a lens of focal length 5 cm. Numerical
    1. Find image distance.
    2. Find linear magnification.
    3. If the slide has a letter of height 2 cm, how tall is the projected image?
  31. (a) Derive the mirror formula $\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$ for a concave mirror with the help of a neat ray diagram showing the geometry clearly.
    (b) An object 5 cm tall is placed 30 cm in front of a concave mirror of focal length 20 cm. Find image distance, image height and nature of image. 5-Mark
  32. (a) State Snell's law of refraction. Derive the relation $n = \dfrac{c}{v}$ where c is speed of light in vacuum and v in medium.
    (b) A ray of light passes through a triangular glass prism. The angle of the prism is 60° and the refractive index of glass is $\sqrt{3}$. Find the angle of minimum deviation. Also find the angle of incidence at minimum deviation. 5-Mark
  33. (a) What is dispersion of light? Explain with a labelled diagram how a glass prism disperses white light into a spectrum (VIBGYOR). Why does violet deviate more than red?
    (b) Isaac Newton performed a famous experiment to show that white light is not pure. Describe how he recombined the spectrum back into white light using a second prism.
    (c) Why does the sky appear blue? Why does the sun appear red at sunrise and sunset? 5-Mark
  34. [Case Study — Camera vs Human Eye] A camera uses a convex lens (f = 5 cm) to form images on a sensor. An object 200 cm tall stands 5 m away. Answer: Case Study
    1. Find height of image on camera sensor. [1]
    2. Name the part of human eye corresponding to: (a) lens; (b) iris/diaphragm; (c) retina; (d) ciliary muscles. [1]
    3. Explain power of accommodation and least distance of distinct vision with a ray diagram showing near-point and far-point. [2]
  35. [Case Study — Ophthalmology] Three patients visit Dr. Priya:
    Patient X: cannot see objects closer than 80 cm.
    Patient Y: cannot see objects farther than 50 cm.
    Patient Z: cannot see clearly at any distance (age: 55 years). Case Study
    1. Name the defect of vision for X, Y and Z. [1]
    2. Find power and type of corrective lens for Patient X. (near point must shift from 80 cm to 25 cm) [1]
    3. Find power and type of corrective lens for Patient Y. (far point must shift from 50 cm to ∞) [1]
    4. What is presbyopia? How is it corrected? [1]
  36. [Case Study — Total Internal Reflection] A telecommunication company uses optical fibres to transmit data at the speed of light over long distances. The core has n = 1.62 and the cladding has n = 1.52. Case Study
    1. Find the critical angle at the core-cladding interface. (sin¹ ≈ use values given) [1]
    2. If a ray strikes the core-cladding boundary at 70°, will it undergo TIR? Justify. [1]
    3. Explain the working principle of an optical fibre with a diagram. [2]
  37. (a) Explain the phenomenon of atmospheric refraction. How does it cause: (i) stars to twinkle; (ii) advance sunrise and delayed sunset?
    (b) An object is placed at the principal focus of a concave mirror of focal length 15 cm. Where is the image formed? Now the object is moved 5 cm closer to the mirror. Find the new image distance. 5-Mark
  38. (a) A convex lens of power +5 D is placed in contact with another lens. The combination has power +3 D. Find the focal length and nature of the second lens.
    (b) An eye has a least distance of distinct vision of 25 cm. Using a convex lens of focal length 5 cm as magnifying glass, find: (i) the maximum magnification; (ii) the position of object for this magnification. 5-Mark
  39. (a) Draw ray diagrams showing the path of light through: (i) a glass prism (dispersion); (ii) a water droplet (rainbow formation). In each case, label all relevant angles and colours.
    (b) A rainbow is seen after rain. In a primary rainbow, which colour appears on the outside arc and which on the inside? Explain the physics behind this arrangement. 5-Mark
  40. (a) Derive the lens formula $\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$ for a convex lens forming a real image, using a ray diagram. Clearly state the sign convention used.
    (b) An object 3 cm high is placed 8 cm from a convex lens of focal length 12 cm. Find image position, height and nature.
    (c) A person uses a bi-focal lens with upper half concave (f = 2 m) and lower half convex (f = 40 cm). Explain the purpose of each half. 5-Mark

⚡ Section 2 — Current Electricity: Ohm's Law, Resistance, Power & Domestic Circuits

Q46–Q90  |  MCQ (Q46–Q55) • Numericals & Short Answer (Q56–Q80) • Long Answer (Q81–Q90)
  1. A wire of resistance R is stretched uniformly until its length is doubled. The new resistance will be: MCQ
    • R/2
    • 2R
    • 4R
    • R/4
  2. A 100 W bulb and a 60 W bulb (both rated 220 V) are connected in series across a 220 V supply. The ratio of power consumed by the 100 W bulb to the 60 W bulb is: MCQ
    • 100:60
    • 60:100
    • 10:6
    • 6:10
  3. Three resistors, each of value R, are connected as shown: two in parallel, and this combination in series with the third. The equivalent resistance of the circuit is: MCQ
    • 3R/2
    • 2R/3
    • 3R
    • R/3
  4. A battery of EMF 10 V and internal resistance 1 Ω is connected to an external resistance of 4 Ω. The terminal voltage of the battery is: MCQ
    • 10 V
    • 8 V
    • 9 V
    • 6 V
  5. Which V–I graph correctly represents a metallic conductor obeying Ohm's law? MCQ
    • A curve (parabolic shape)
    • A straight line through origin
    • A horizontal straight line
    • A vertical straight line
  6. Two bulbs: P = 40 W at 220 V and Q = 100 W at 220 V are connected in parallel to a 220 V supply. The current through the 40 W bulb compared to the 100 W bulb is: MCQ
    • More
    • Less
    • Equal
    • Zero
  7. An electric heater rated 2 kW is used for 3 hours. The electrical energy consumed in kWh and in joules is: MCQ
    • 6 kWh; 2.16×107 J
    • 6 kWh; 6×103 J
    • 0.6 kWh; 2.16×106 J
    • 6 kWh; 6×106 J
  8. Assertion (A): Resistivity of a conductor increases with temperature.
    Reason (R): At higher temperature, lattice vibrations of ions increase, causing more frequent collisions for free electrons, thus impeding their flow. A&R
    A: Resistivity of metallic conductors increases with rise in temperature.
    R: Increased lattice vibrations at higher temperatures scatter free electrons more frequently, increasing resistivity.
    1. Both A and R are true, and R is the correct explanation of A.
    2. Both A and R are true, but R is NOT the correct explanation.
    3. A is true but R is false.
    4. A is false but R is true.
  9. Assertion (A): In a parallel circuit, the equivalent resistance is always less than the smallest individual resistance.
    Reason (R): When resistors are connected in parallel, more paths are provided for current, decreasing total resistance. A&R
    A: Equivalent resistance of a parallel combination is always less than the smallest individual resistance.
    R: Additional parallel paths increase total conductance, so resistance decreases below any individual value.
    1. Both A and R are true, and R is the correct explanation of A.
    2. Both A and R are true, but R is NOT the correct explanation.
    3. A is true but R is false.
    4. A is false but R is true.
  10. Assertion (A): Fuse wire must always be connected in the live wire of a domestic circuit.
    Reason (R): A fuse is a safety device that melts due to excessive current, breaking the circuit before damage occurs. It must be on the live side for safety. A&R
    A: Fuse wire is connected in the live wire in a domestic circuit, not in the neutral wire.
    R: Connecting fuse in the live wire ensures the appliance is disconnected from the high potential when fuse blows, preventing shock.
    1. Both A and R are true, and R is the correct explanation of A.
    2. Both A and R are true, but R is NOT the correct explanation.
    3. A is true but R is false.
    4. A is false but R is true.
  11. A wire of nichrome (resistivity ρ = 1.0 × 10−6 Ω·m) has length 1.5 m and cross-sectional area 1.5 × 10−6 m2. Numerical
    1. Calculate the resistance of the wire.
    2. If a potential difference of 6 V is applied, find the current.
    3. Find the power dissipated in the wire.
  12. Three resistors R1 = 4 Ω, R2 = 6 Ω, R3 = 12 Ω are connected in parallel across a 12 V battery. Numerical
    1. Find the equivalent resistance.
    2. Find the current through each resistor.
    3. Find the total current drawn from the battery.
    4. Find the power dissipated in each resistor and total power.
  13. A circuit consists of a 4 Ω resistor in series with a parallel combination of 6 Ω and 3 Ω, connected to a 12 V battery. Find: Numerical
    12V 4 Ω Series 6 Ω 3 Ω A B
    1. Equivalent resistance of circuit.
    2. Total current from battery.
    3. Current through the 6 Ω and 3 Ω resistors.
    4. Voltage drop across the 4 Ω series resistor.
    5. Power dissipated in the parallel combination.
  14. A wire of resistance 8 Ω is stretched to 4 times its original length. Assuming volume is constant: Numerical
    1. Find the new resistance.
    2. If the original wire carries 3 A, find the new current when connected to the same voltage source.
    3. Find the ratio of power dissipated before and after stretching.
  15. Two resistors P = 6 Ω and Q = 4 Ω are connected in series to a 20 V source. They are then reconnected in parallel to the same source. Compare: Numerical
    1. Total current in series vs parallel.
    2. Current through P in series vs parallel.
    3. Power dissipated in series vs parallel.
    4. In which case does Q consume more power?
  16. An electric heater of resistance 4 Ω and a lamp of resistance 6 Ω are connected in parallel. This parallel combination is connected in series with a 10 Ω resistance and a 40 V supply. Numerical
    1. Draw the circuit diagram using SVG (done in solution). Find equivalent resistance.
    2. Find total current from source.
    3. Find current through heater and lamp separately.
    4. Find voltage across the parallel combination.
  17. An electric iron consumes 840 W at 220 V. Numerical
    1. Find the resistance of the heating element.
    2. Find the current through it.
    3. Find the heat produced in 30 minutes.
    4. Find the cost of electricity for 30 min daily use for 1 month (30 days) at ›6 per kWh.
  18. A 100 W, 250 V bulb is connected to a 200 V supply. Find: Numerical
    1. Resistance of the bulb filament.
    2. Current through the bulb at 200 V.
    3. Actual power consumed at 200 V.
    4. Ratio of actual power to rated power.
  19. Three identical bulbs (each 60 W, 220 V) are connected: first all three in parallel across 220 V, then all three in series across 220 V. Numerical
    1. Find power consumed by each bulb in parallel combination.
    2. Find power consumed by each bulb in series combination.
    3. In which combination do the bulbs glow brighter? Justify.
    4. Find the ratio of total power consumed in parallel vs series.
  20. A battery of EMF 12 V has an internal resistance of 2 Ω. It is connected to an external resistor of 10 Ω. Numerical
    1. Find the current in the circuit.
    2. Find the terminal voltage of the battery.
    3. Find the power delivered to the external resistor.
    4. Find the power wasted in internal resistance and efficiency of the battery.
  21. A household has the following appliances: refrigerator (200 W, 24 h/day), two fans (75 W each, 12 h/day), three LED bulbs (10 W each, 8 h/day), TV (120 W, 5 h/day), electric iron (1000 W, 1 h/day), geyser (2000 W, 0.5 h/day). Electricity rate: ›7/unit. Numerical
    1. Calculate total energy consumed per day in kWh.
    2. Calculate the monthly electricity bill (30 days).
    3. If the geyser is replaced by a solar water heater, find annual savings.
  22. A conducting wire has resistance R0 at 0°C. At temperature t°C, resistance becomes R = R0(1 + αt), where α is temperature coefficient of resistance. A nichrome wire has R0 = 10 Ω and α = 0.0004 /°C. Numerical
    1. Find resistance at 200°C.
    2. Find the temperature at which resistance becomes 12 Ω.
    3. Find the percentage increase in resistance when heated from 0°C to 500°C.
  23. A circuit has resistors in the following arrangement: R1=2Ω in series with [R2=6Ω parallel to R3=3Ω] in series with R4=4Ω, all connected to a 20V battery. Numerical
    1. Find equivalent resistance of the entire circuit.
    2. Find total current from battery.
    3. Find potential difference across the parallel combination.
    4. Find current through R2 and R3.
    5. Find power dissipated in R4.
  24. [Competency-Based] Priya's hostel room has: a 100W fan (8 h/day), a 40W bulb (5 h/day), and a 1200W hair dryer (0.25 h/day). The 5A MCB in her room trips every day at the same time. The supply is 220V. Competency
    1. Calculate total current when all appliances run simultaneously.
    2. Why does the MCB trip? Identify which appliance causes it.
    3. Suggest a solution to prevent the MCB from tripping.
    4. Calculate monthly electricity bill for her room at ›8/kWh (30 days).
  25. A 60W, 220V bulb and a 100W, 220V bulb are connected in series to a 440V supply. Find: Numerical
    1. Resistance of each bulb.
    2. Current through the series circuit.
    3. Power consumed by each bulb.
    4. Which bulb is more likely to fuse? Why?
  26. An incandescent bulb is rated 60W at 220V. An LED rated 9W at 220V gives equivalent light output. A family replaces 8 such incandescent bulbs with LEDs. Numerical
    1. Find the resistance of each type of bulb.
    2. If all 8 incandescent bulbs were on for 6 hours daily, find the daily energy consumed.
    3. Find daily energy consumed by 8 LEDs for 6 hours.
    4. Find annual savings in money at ›5/kWh (365 days).
  27. (a) Derive the expression for equivalent resistance of n resistors connected in parallel. Hence prove that equivalent resistance in parallel is always less than each individual resistance.
    (b) Five resistors of 10 Ω each are connected. Find the maximum and minimum possible equivalent resistances using all five. 5-Mark
  28. (a) State Joule's law of heating. Derive the expression $H = I^2 R t = \dfrac{V^2 t}{R} = VIt$.
    (b) An electric kettle has a coil of resistance 44 Ω connected to 220 V supply. It takes 10 minutes to boil 500 g of water from 30°C. Find: (i) current; (ii) heat produced; (iii) specific heat capacity of water if all heat goes to water. (c = 4200 J/kg°C; final temp = 100°C) 5-Mark
  29. (a) Explain the concept of electric power. Derive P = VI = I2R = V2/R.
    (b) A motor operates at 220V and draws 10A. If 80% of the electrical power is converted to mechanical power, find: (i) electrical power input; (ii) mechanical power output; (iii) heat generated per hour; (iv) cost of running for 8 hours at ›6/kWh. 5-Mark
  30. [Case Study — Solar-Powered School] A school installs solar panels generating 230V DC. The school needs to power: 10 ceiling fans (75W each), 40 LED tubes (18W each), 5 computers (300W each), and a water pump (750W). All appliances run in parallel on 230V. Case Study
    1. Find total power consumption of the school. [1]
    2. Find total current drawn from the 230V supply. [1]
    3. If the school runs for 8 h/day, 200 days/year, find annual energy consumed in kWh. [1]
    4. Solar panels each generate 250W. How many panels are needed? [1]
  31. [Case Study — Domestic Safety] A 220V domestic supply serves a living room. A refrigerator (200W), TV (150W), AC (1500W) and two fans (75W each) are connected in parallel via a 15A MCB. Case Study
    1. Find total current when all appliances run together. Will the 15A MCB trip? [1]
    2. Explain: (a) overloading; (b) short circuit; (c) why earth wire is necessary. [2]
    3. Find monthly electricity bill (8 h/day, 30 days, ›7/kWh). [1]
  32. (a) Explain with diagram the principle and working of an electric fuse. What properties should the fuse wire material have?
    (b) Four resistors: A=2Ω, B=3Ω, C=6Ω, D=1Ω are connected to a 12V battery as follows: A in series with (B parallel C) in series with D. Find: (i) Req; (ii) total current; (iii) current through B; (iv) power dissipated in C; (v) terminal voltage if battery has internal resistance 1Ω. 5-Mark
  33. (a) A student plots a V–I graph for three resistors X, Y, Z (same material, different dimensions). X has the steepest slope, Z has the gentlest. Arrange X, Y, Z in order of: (i) increasing resistance; (ii) increasing resistivity; (iii) which has longest length (if area is same).
    (b) X, Y, Z are connected in parallel to a 6V battery. Total current = 6A. Find: (i) Req; (ii) if X = 2Ω, Y = 3Ω, find Z; (iii) power in Z. 5-Mark
  34. (a) Define resistivity. Write the formula and SI unit. Explain its dependence on temperature for (i) metals; (ii) semiconductors; (iii) alloys like Nichrome.
    (b) A nichrome wire (resistivity = 1.2×10−6 Ω·m) of diameter 0.6 mm is required to produce a 30 Ω resistor. Find its required length. (π = 3.14)
    (c) Why is nichrome used in heating elements but not in electrical transmission lines? 5-Mark
  35. [Competency-Based] Rahul connects three identical batteries (EMF = 2V, internal resistance r = 0.5Ω each): Case A — all in series; Case B — all in parallel; external load R = 3Ω in each case. 5-Mark
    1. Find EMF and internal resistance of combination in each case.
    2. Find current through external load in each case.
    3. Find terminal voltage across load in each case.
    4. Find power delivered to load in each case.
    5. In which case does each battery supply more current? Why is parallel preferred for high-current low-resistance loads?
  36. (a) Explain the construction and working of a domestic electric circuit with a diagram, showing: live wire, neutral wire, earth wire, MCB, meter, and branch circuits.
    (b) Why are domestic appliances connected in parallel and not in series? Give three scientific reasons.
    (c) A short circuit occurs in a 220V domestic line. If the fuse has resistance 0.1Ω, find the current that flows in the short-circuit before the fuse blows (short-circuit wire resistance ≈ 0.1Ω). 5-Mark
  37. [Competency-Based — Real World] An EV (Electric Vehicle) battery pack is rated at 48V, 100 Ah (ampere-hour). The motor draws 20A at 48V during normal driving. 5-Mark
    1. Find total energy stored in the battery in kWh.
    2. Find the range (driving time) on a full charge at normal speed.
    3. The battery is made of 16 identical cells in series. Find EMF and capacity of each cell.
    4. Charging takes 4 hours at 50V with 15A. Find cost of one full charge at ›8/kWh.
    5. If 10% energy is lost as heat in motor winding (R = 0.5Ω per phase), find heat generated per hour of driving.

✅ Quick Answer Key — MCQ & Assertion-Reason (Q1–Q15 and Q46–Q55)

Q.Answer (Light)Q.Answer (Current)
1(b) Virtual, erect, magnified [object inside F]46(c) 4R [R ∝ l²/V; l doubles ⇒ R×4]
2(a) 40 cm beyond concave lens47(b) 60:100 [series: same I; P=I²R; R100W<R60W]
3(c) ~1.6 cm [d=t·sin(i−r)/cos r]48(a) 3R/2 [two R in parallel = R/2; +R series = 3R/2]
4(a) −1.25 D [myopia correction only]49(b) 8V [I=10/5=2A; VT=10−2×1=8V]
5(a) Highest refractive index ⇒ smallest critical angle50(b) Straight line through origin
6(b) Full image, but dimmer51(b) Less [I=P/V; 40W bulb draws less current]
7(c) Frequency [frequency unchanged during refraction]52(a) 6 kWh; 2.16×107 J
8(a) At C, real, inverted, same size53(a) Both true; R is correct explanation
9(c) Plane glass (no effect)54(a) Both true; R is correct explanation
10(a) Both true; R is correct explanation55(a) Both true; R is correct explanation
11(a) Both true; R is correct explanation——
12(a) Both true; R is correct explanation——
13(a) +60 cm to −17.1 cm——
14(c) Both myopic and hypermetropic——
15(b) 400 nm [λ = λair/n = 600/1.5]——

For complete step-by-step solutions, worked numericals, and SVG diagrams for all 90 questions — refer to:
Light and Current Practice1Solution.html