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ICSE Class 10 Physics (Science Paper – 1) Solved Paper 2026

Complete ICSE Class X Physics 2026 question paper with accurate, step-by-step solutions.

ICSEClass XPhysics202680 Marks2 h43 Questions

Question 1 of 43

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Section A (40 Marks)

(Attempt all questions from this section)

Question 1 (i)

1 (i)ForceEasy1 Mark

For a body to be in dynamic equilibrium:

Answer

(b) Its acceleration must be zero.

Explanation:

A body in dynamic equilibrium moves with uniform velocity. Therefore, its acceleration is zero.

Question 1 (ii)

1 (ii)Work, Energy and PowerEasy1 Mark

The energy transformation that takes place during photosynthesis is:

Answer

(c) Light energy to chemical energy.

Explanation:

During photosynthesis, plants convert light energy from the Sun into chemical energy stored in food.

Question 1 (iii)

1 (iii)MachinesEasy1 Mark

The velocity ratio of a block and tackle system having two pulleys, with effort applied upwards, is:

Answer

(c) 3

Explanation:

When the effort is applied upwards, one end of the rope is fixed to the movable block. The number of supporting rope segments is three, so the velocity ratio is 3.

Question 1 (iv)

1 (iv)Refraction of Light at Plane SurfacesModerate1 Mark

The diagram shows a ray of light travelling from medium A to medium B.

The diagram shows a ray of light travelling from medium A to medium B

The refractive index of medium B with respect to medium A is:

Answer

(d) \frac{\sin 60^\circ}{\sin 45^\circ}

Explanation:

The diagram shows a ray of light travelling from medium A to medium B 2

The angle of incidence = 60° and

the angle of refraction = 45°.

Therefore, refractive index of B with respect to A = \frac{\sin 60^\circ}{\sin 45^\circ}.

Question 1 (v)

1 (v)SpectrumEasy1 Mark

A blackened thermometer bulb placed beyond the red end of a spectrum shows a rise in temperature due to:

Answer

(a) Infrared radiations.

Explanation:

Infrared radiations lie beyond the red end of the visible spectrum and produce a strong heating effect.

Question 1 (vi)

1 (vi)Work, Energy and PowerEasy1 Mark

A cyclist stops pedalling while moving along a frictionless hilly road. Which quantity remains constant?

Answer

(d) Total mechanical energy remains constant.

Explanation:

In the absence of friction, kinetic energy and potential energy interchange while their sum remains constant.

Question 1 (vii)

1 (vii)Refraction Through a LensEasy1 Mark

The distance of a virtual image formed by a lens of focal length 15 cm can never exceed:

Answer

(d) 15 cm.

Explanation:

For a concave lens, the virtual image is always formed between the optical centre and the principal focus. Hence its distance cannot exceed the focal length.

Question 1 (viii)

1 (viii)SpectrumModerate1 Mark

Assertion: Tiny air molecules scatter blue light more than red light.

Reason: The refractive index of air is greater for blue light than for red light.

Answer

(d) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

Explanation:

Blue light is scattered more strongly because scattering varies inversely as the fourth power of wavelength. The stated refractive-index relation does not explain this scattering.

Question 1 (ix)

1 (ix)Current ElectricityModerate1 Mark

Study the circuit diagram containing lamps L1, L2, L3 and L4.

Study the circuit diagram containing lamps L1 L2 L3 and L4

Which lamp can fail without interrupting the glow of the other lamps?

Answer

(b) L2

Explanation:

L2 is connected in a separate parallel branch. Its failure does not break the paths through the other lamps.

Question 1 (x)

1 (x)SoundModerate1 Mark

Three cylindrical jars A, B and C contain equal volumes of water up to different heights. Their radii satisfy rB < rA < rC.

Which jar produces the shrillest sound when air is blown across its mouth?

Answer

(b) B

Explanation:

For the same volume of water, the jar with the smallest radius has the greatest water height and therefore the shortest air column. A shorter air column produces a higher frequency and a shriller sound.

Question 1 (xi)

1 (xi)CalorimetryEasy1 Mark

When the length of a stretched metallic wire is doubled, its specific heat:

Answer

(d) Remains the same.

Explanation:

Specific heat capacity is a property of the material and does not depend on its dimensions.

Question 1 (xii)

1 (xii)Current ElectricityModerate1 Mark

The equivalent resistance of two resistors R1 and R2 connected in parallel is:

Answer

(b) \frac{\mathrm{R}_1\mathrm{R}_2}{\mathrm{R}_1+\mathrm{R}_2}

Explanation:

For two parallel resistors, \frac{1}{\mathrm{R}}=\frac{1}{\mathrm{R}_1}+\frac{1}{\mathrm{R}_2}.

Question 1 (xiii)

1 (xiii)Electro-magnetismModerate1 Mark

The diagram shows two compasses near a straight wire carrying current into the plane of the paper.

compass-alignment-around-current-carrying-wire

Which compass is correctly aligned?

Answer

(a) Only compass 1.

Explanation:

For current into the plane of the paper (×), the right-hand thumb rule gives a clockwise magnetic field.

Compass 1 is tangent to the field and points in the correct direction, whereas compass 2 points opposite to the field direction.

Therefore, only compass 1 is correctly aligned.

Question 1 (xiv)

1 (xiv)CalorimetryModerate1 Mark

Equal masses of substances A, B and C, each at its melting point, take 5 minutes, 7 minutes and 3 minutes respectively to melt when heated at the same rate. Which has the highest specific latent heat of fusion?

Answer

(b) B

Explanation:

For equal masses heated at the same rate, the substance taking the longest time absorbs the greatest latent heat.

Question 1 (xv)

1 (xv)RadioactivityEasy1 Mark

A lithium atom has 3 electrons, 3 protons and 4 neutrons. Its mass number is:

Answer

(c) 7

Explanation:

Mass number = number of protons + number of neutrons = 3 + 4 = 7.

Question 2 (i)

2 (i)ForceModerate6 Marks

Complete the following by choosing the correct answers from the bracket:

(a) A car is moving in uniform circular motion. The direction of friction between the tyres and the path is …………… [towards the centre / tangential to the path].

(b) When a ray of light passes from a denser to a rarer medium, its wavelength …………… [decreases / increases].

(c) The lid of a calorimeter minimises heat loss by …………… [convection / radiation].

(d) Quality of sound depends on its …………… [amplitude / waveform].

(e) A substance whose resistance becomes almost negligible at a temperature near absolute zero is called a …………… [semiconductor / superconductor].

(f) …………… radiation deviates minimum in a magnetic field [Alpha / Beta].

Answer

(a) tangential to the path

(b) increases

(c) convection

(d) waveform

(e) superconductor

(f) Alpha

Question 2 (ii)

2 (ii)ForceEasy2 Marks

State two factors on which the position of Center of Gravity of a body depends.

Answer

The position of the centre of gravity of a body depends mainly on two factors:

  1. Shape of the body
  2. Distribution of mass in the body

Explanation:

The position of the centre of gravity depends on the shape of the body and on how its mass is distributed. For example, two rods may have the same shape and size, but if one rod is uniform and the other is heavier at one end, their centres of gravity will be at different positions.

Question 2 (iii)

2 (iii)MachinesModerate2 Marks
  • Case 1: Lata cuts a potato into two halves, using a cutter which belongs to a Class II lever. She needed effort E1.
  • Case 2: Then she cuts one half of this potato again, but this time she needed effort E2. If E1 > E2 then:

(a) In which case (1st or 2nd) was the potato closer to her hand applying the effort? (Assume normal reaction of the surface of the potato is same in both cases)

(b) Give a reason for your answer in (a) above.

Answer

(a) The potato was closer to her hand in Case 1.

(b) The cutter acts as a Class II lever, in which the load lies between the fulcrum and the effort. When the potato is placed closer to the hand applying effort, it is farther from the fulcrum, so the load arm becomes longer. For a fixed effort arm, a longer load arm requires greater effort to cut. Since E1 > E2, the potato must have been closer to her hand in Case 1.

Question 3 (i)

3 (i)Refraction Through a LensEasy2 Marks

The graph below shows the variation of image distance (v) with the object distance (u) when an object is kept in front of a lens.

image-distance-vs-object-distance-lens-graph

(a) Identify the type of lens used.

(b) What would be the magnification (more than 1 / less than 1 / equal to 1) if the object is placed between F and 2F of the above lens?

Answer

(a) The lens used is a convex lens.

(b) If the object is placed between F and 2F, the magnification will be more than 1.

Explanation:

(a) The graph shows that for an object placed in front of the lens, a real image is formed on the other side and the image distance changes according to the position of the object. This behaviour is shown by a convex lens.

(b) For a convex lens, when the object is placed between F and 2F, the image is formed beyond 2F. The image is real, inverted and magnified. Therefore, the magnification is more than 1.

Question 3 (ii)

3 (ii)Current ElectricityEasy2 Marks

A resistance R is connected across a cell with a switch and a rheostat in series. A voltmeter is connected parallel across the cell. Current in the circuit is increased using the rheostat.

(a) How will the voltmeter reading change? (increase / decrease / remain the same)

(b) Justify your answer stated in (a) above.

Answer

(a) The voltmeter reading decreases.

(b) The voltmeter reading is given by: V = ε – Ir

where I is the current flowing in the circuit, ε is the emf of the cell and r is the internal resistance of the cell.

When the rheostat is adjusted to increase the current in the circuit, the current drawn from the cell becomes larger. Due to the internal resistance of the cell, a greater potential drop occurs inside the cell.

As a result, the terminal voltage of the cell decreases. Since the voltmeter measures this terminal voltage across the cell, its reading decreases.

Question 3 (iii)

3 (iii)SoundEasy2 Marks

(a) Define natural vibrations.

(b) How is this vibration different from damped vibrations in terms of their amplitudes?

Answer

(a) The periodic vibrations of a body in the absence of any external force on it are called natural (or free) vibrations.

(b) In natural vibrations, the amplitude remains constant because there is no loss of energy, while in damped vibrations the amplitude gradually decreases with time due to energy loss caused by the presence of resistive force.

Question 3 (iv)

3 (iv)CalorimetryEasy2 Marks

A metal piece of thermal capacity 40 J K−1 absorbs 800 J of heat. Calculate the rise in the temperature of this metal piece.

Answer

Given,

Thermal capacity = 40 J K−1

Heat absorbed = 800 J

Let the rise in temperature be T.

Temperature rise = \frac{\text{Heat absorbed}}{\text{Thermal capacity}}

T = \frac{800}{40} = 20 K

Since a rise of 1 K = 1°C, the rise in temperature is also 20°C.

Hence, the rise in the temperature of the metal piece is 20°C.

Question 3 (v)

3 (v)Electro-magnetismEasy2 Marks

In an AC generator, name the part which has the following functions:

(a) intensifies the magnetic field.

(b) maintains electrical contact between the rotating parts and the external circuit.

Answer

(a) Soft iron core

(b) Carbon brushes

Question 3 (vi)

3 (vi)RadioactivityEasy2 Marks

Give two differences between nuclear fission and nuclear fusion.

Answer
Nuclear fission Nuclear fusion
(a) Nuclear fission is the process of breaking a heavy nucleus into two nearly equal fragments with the release of energy. Nuclear fusion is the process of combining light nuclei to form a larger nucleus at a very high temperature and pressure with the release of energy.
(b) This reaction is possible at ordinary temperature and ordinary pressure. This reaction is possible only at a very high temperature (approximately 107 K) and a very high pressure.

Question 3 (vii)

3 (vii)Refraction of Light at Plane SurfacesEasy3 Marks

A monochromatic ray strikes the surface of identical prisms (A, B and C) at different angles of incidence. The diagram below shows their refracted rays. Study the path of these refracted rays and identify in which of the diagrams:

refracted-rays-in-identical-prisms

(a) the angle of incidence is maximum.

(b) the angle of incidence is minimum.

(c) the angle of incidence is equal to the angle of emergence.

Answer

(a) The angle of incidence is maximum for prism B.

(b) The angle of incidence is minimum for prism A.

(c) The angle of incidence is equal to the angle of emergence for prism C.

Explanation:

For identical prisms, a larger angle of incidence produces a refracted ray inside the prism making a larger angle with the normal. Hence, diagram B corresponds to maximum incidence, while diagram A corresponds to minimum incidence.

When the angle of incidence is equal to the angle of emergence, the path of the ray through the prism is symmetrical, and the refracted ray inside the prism becomes parallel to the base. This is shown in diagram C.

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Section B (40 Marks)

(Attempt any four questions)

Question 4 (i)

4 (i)Refraction of Light at Plane SurfacesModerate3 Marks

A ray of light enters a glass block from air and comes out from the opposite surface. If the angle of refraction at the first surface is not the same as the angle of incidence at the second surface, then:

(a) What is the product of the ratio sin i / sin r at the first surface and at the second surface?

(b) State whether the opposite surfaces are parallel or not parallel.

(c) How did you reach the conclusion in (b) above?

Answer

(a) At the first surface, from air to glass:

\frac{\sin \mathrm{i_1}}{\sin \mathrm{r_1}} = μ

At the second surface, from glass to air:

\frac{\sin \mathrm{i_2}}{\sin \mathrm{r_2}}=\frac{1}{\text{μ}}

Therefore, the product is \mu\times\frac{1}{\text{μ}}=1.

(b) The opposite surfaces are not parallel.

(c) If the opposite surfaces were parallel, the angle of refraction at the first surface would equal the angle of incidence at the second surface. Since these angles are not equal, the surfaces cannot be parallel.

Question 4 (ii)

4 (ii)Refraction of Light at Plane SurfacesModerate3 Marks

A type of glass block has a refractive index of 1.8.

(a) Calculate the speed of light in this glass. (Given speed of light in air = 3 × 108 m s−1)

(b) If the width of this block is doubled, then what will be the speed of light in the block?

Answer

(a) Given, refractive index of the glass block = 1.8 and speed of light in air = 3 × 108 m s−1.

Speed of light in glass = \frac{3\times10^8}{1.8} = 1.67 × 108 m s−1.

(b) If the width of the glass block is doubled, the speed of light does not change because it depends on the refractive index of the material, not its thickness.

Therefore, the speed remains 1.67 × 108 m s−1.

Question 4 (iii)

4 (iii)SpectrumModerate4 Marks

(a) Name the electromagnetic radiation used to detect fake currency.

(b) Redraw the diagram given below and complete the path of the light ray AB through the glass prism till it emerges out of the prism. Critical angle of the glass is 42°.

complete-light-ray-path-through-prism

Answer

(a) Ultraviolet (UV) radiation

(b) The completed diagram is shown below

complete-light-ray-path-through-prism-answer

Explanation:

The ray AB enters the prism normally at point B, so it passes straight into the prism without bending. It then strikes the slant face with an angle of incidence of 60°. Since 60° is greater than the critical angle of 42°, the ray undergoes total internal reflection. It then reaches the opposite face with an angle of incidence of 30°, which is less than the critical angle, and refracts out of the prism.

Question 5 (i)

5 (i)Refraction Through a LensHard3 Marks

An object placed in front of a convex lens forms an image of the same size on a screen. Moving the object 12 cm closer to the lens results in the formation of a real image which is three times the size of the object. Calculate the focal length of the lens.

Answer

Initially, the real image is the same size, so magnification = −1 and u = −v.

From the lens formula:

\frac{1}{\mathrm{f}}=\frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}=\frac{2}{\mathrm{v}}

Therefore, v = 2f.

After moving the object 12 cm closer, u′ = u + 12 and magnification = −3. Hence, v′ = 3v − 36.

For the final position:

\frac{1}{\mathrm{f}}=\frac{1}{\mathrm{v'}}-\frac{1}{\mathrm{u'}}=\frac{4}{\mathrm{v'}}

Therefore, f = v′/4 = (3v − 36)/4.

Using v = 2f:

f = \frac{6\mathrm{f}-36}{4}

Hence, f = 18 cm.

Question 5 (ii)

5 (ii)CalorimetryModerate3 Marks

(a) Atmospheric temperature after a hailstorm is greater than the temperature during the hailstorm. State True or False.

(b) Which thermal physical quantity of a frying pan changes by making its base heavier?

(c) State the principle of Calorimetry.

Answer

(a) False

Explanation:

After the hailstorm, ice absorbs the heat energy required for melting from the surroundings, so the temperature of the surroundings falls further.

(b) Making the base heavier increases its heat capacity because heat capacity depends on mass.

(c) The principle of calorimetry states that when a hot body is brought in contact with a cold body, heat lost by the hot body equals heat gained by the cold body, provided there is no heat loss to the environment.

Question 5 (iii)

5 (iii)CalorimetryModerate4 Marks

The given graph represents the cooling curve of a liquid.

cooling-curve-of-a-liquid

(a) State the freezing temperature of the liquid.

(b) Name the phase change happening at the region QR.

(c) In which state (solid / liquid) does the above substance liberate heat at a faster rate? Justify.

Answer

(a) The freezing temperature is 20°C because the graph becomes horizontal at this temperature.

(b) The phase change in region QR is freezing, where the liquid changes into solid.

(c) The substance liberates heat faster in the solid state. The graph after point R has a steeper slope, indicating a faster decrease in temperature than in the liquid state before point Q.

Question 6 (i)

6 (i)ForceModerate3 Marks

The diagram shows a wheel with a handle. Two forces, F1 and F2 of equal magnitudes are acting on the handle as shown in the diagram.

equal-forces-on-wheel-handle

(a) Which force produces negative moment?

(b) Is the wheel in equilibrium? (Yes or No)

(c) Justify your answer stated in (b).

Answer

(a) Force F1 produces the negative moment because it tends to rotate the wheel clockwise.

(b) No, the wheel is not in equilibrium.

(c) For equilibrium, the sum of clockwise moments must equal the sum of anticlockwise moments about the centre O. Although F1 and F2 have equal magnitudes, their perpendicular distances from the centre are different. Therefore, their moments are not equal and opposite, the net moment is not zero, and the wheel is not in equilibrium.

Question 6 (ii)

6 (ii)Work, Energy and PowerModerate3 Marks

(a) Name the unit of work done used on the subatomic scale.

(b) To which class of lever does a pair of scissors belong?

(c) A stone is tied to a string and displaced from A to B by application of constant force F in three different ways as shown below.

stone-displaced-by-constant-force-three-paths

Arrange the three cases in ascending order of the work done by the force. (Given AJB is a semicircle, θ < 90° and AB = 20 m)

Answer

(a) electron volt (eV)

(b) Class I lever

(c) Work done is W = Force × Displacement × cos θ.

In Case 1, force is perpendicular to displacement, so work done is zero.

In Case 2, force acts along displacement, so work done is maximum.

In Case 3, θ < 90°, so the work done is greater than Case 1 but less than Case 2.

Therefore, the ascending order is: Case 1 < Case 3 < Case 2.

Question 6 (iii)

6 (iii)Work, Energy and PowerModerate4 Marks

A ball of mass 20 g falls from a height of 45 m. It rebounds from the ground to a height of 40 m. Calculate:

(a) initial potential energy of the ball.

(b) the speed of the ball at which it hits the ground.

(c) the loss in kinetic energy on striking the ground.

[g = 10 m s−2]

Answer

Given,  Mass (m) = 20 g = 0.02 kg,

Initial height (h1) = 45 m,

Rebound height (h2) = 40 m and g = 10 m s−2.

(a) Initial potential energy = mgh1 = 0.02 × 10 × 45 = 9 J.

(b) Just before hitting the ground:

\frac{1}{2}\mathrm{mv^2}=9

v = \sqrt{900} = 30 m s−1.

(c) Kinetic energy after rebound = 0.02 × 10 × 40 = 8 J.

Loss in kinetic energy = 9 − 8 = 1 J.

Question 7 (i)

7 (i)MachinesModerate3 Marks

To lift a load of 30 kgf, Suhas uses a single fixed pulley while Radha uses a single movable pulley. The displacement of efforts in both cases is equal. In an ideal situation calculate the ratio of:

(a) the efforts in the two cases.

(b) the potential energy gained by the loads in the two cases.

(c) the efficiencies in the two cases.

Answer

Given,

Load = 30 kgf

(a) Mechanical advantage (MA) of a machine is:

\mathrm{MA}=\frac{\mathrm{Load}}{\mathrm{Effort}}

For a single fixed pulley, MA = 1.

\mathrm{E_1}=\frac{\mathrm{Load}}{\mathrm{MA}}=\frac{30}{1}=30\ \mathrm{kgf}

For a single movable pulley, MA = 2.

\mathrm{E_2}=\frac{\mathrm{Load}}{\mathrm{MA}}=\frac{30}{2}=15\ \mathrm{kgf}

Ratio of efforts = E1 : E2 = 30 : 15 = 2 : 1.

Hence, the ratio of the efforts in the two cases is 2 : 1.

(b) Potential energy gained = Load × Height raised.

If the effort displacement is the same:

  • In a fixed pulley, the load rises through the same distance as the effort.
  • In a movable pulley, the load rises through half the distance moved by the effort.

Let the load in the fixed-pulley case rise through height h. The load in the movable-pulley case rises through h/2.

Ratio of potential energies:

\frac{30\times\mathrm{h}}{30\times\frac{\mathrm{h}}{2}}=\frac{2}{1}=2:1

Hence, the ratio of the potential energies gained by the loads is 2 : 1.

(c) In an ideal machine, efficiency = 100% for both pulleys.

Therefore, the ratio of their efficiencies is 1 : 1.

Question 7 (ii)

7 (ii)SoundEasy3 Marks

(a) One end of a plastic foot ruler is held tightly at the edge of a table and the other end is plucked. Name the vibrations produced in the ruler.

(b) Now the ruler is pushed inside partially and plucked again from its free end. State with a reason whether the frequency of vibration increases or decreases.

Answer

(a) The ruler produces natural vibrations.

(b) The frequency increases because pushing the ruler further inside decreases the length of its free vibrating part. A shorter vibrating length oscillates more rapidly.

Question 7 (iii)

7 (iii)SoundModerate4 Marks

Two persons A and B are standing in front of a cliff in the same line, 170 m apart, as shown in the diagram.

echo-from-cliff-persons-a-and-b-170m-apart

Person B fires a gun and hears the echo in 3 s. Then person A, standing in front of B, fires the gun. (Speed of sound in air = 340 m s−1)

(a) Calculate: (1) the distance of B from the cliff; (2) the minimum time in which B hears the gunshot fired by A.

(b) Fill in the blank: The echo is softer than the original sound due to the decrease in …………… [amplitude / frequency] of the wave.

Answer

Given

  • Distance between A and B = 170 m
  • Time taken by the person B to hear the echo = 3 s
  • Speed of sound in air = 340 ms-1

(a) (1) Distance of B from the cliff = \frac{340\times3}{2} = 510 m.

(a) (2) Minimum time = \frac{170}{340} = 0.5 s.

(b) The echo is softer (less loud) than the original sound due to the decrease in amplitude of the wave.

Question 8 (i)

8 (i)Current ElectricityModerate3 Marks

Bulb A rated 160 W, 40 V and Bulb B rated 40 W, 40 V are connected as shown in the diagram.

bulbs-a-and-b-with-parallel-voltmeters

(a) Calculate the ratio V1 : V2.

(b) If bulb A fuses, the current in the circuit remains the same. State True or False.

Answer

(a) Resistance of bulb A = \frac{40^2}{160} = 10 Ω.

Resistance of bulb B = \frac{40^2}{40} = 40 Ω.

Since the bulbs are in series, potential difference divides in the ratio of resistance.

V1 : V2 = 10 : 40 = 1 : 4.

(b) False

Explanation:

If bulb A fuses, the circuit becomes open and the current becomes zero.

Question 8 (ii)

8 (ii)Household CircuitsModerate3 Marks

The reverse side of a three-pin plug with incorrect connection of wires is shown below.

three-pin-plug-incorrect-wire-connection

(a) Identify the fault in the above connection.

(b) Mention a risk factor involved if the user operates the appliance without correcting it.

(c) Will the appliance function in the present situation? (Yes or No)

Answer

(a) The live red wire is connected to the earth terminal, and the green earth wire is connected to the live terminal. The live and earth wires should be interchanged.

(b) The appliance’s outer metallic body may become live, creating a risk of electric shock.

(c) No, the appliance will not function because the wiring connections are incorrect.

Question 8 (iii)

8 (iii)Current ElectricityHard4 Marks

In the combinations of resistors shown below, calculate:

resistor-combination-with-central-switch

(a) the resistance across AB when switch S is open.

(b) the resistance across AB when switch S is closed.

Answer

(a) When the switch is open, the middle connection does not join the two branches. Therefore, the circuit has two separate branches in parallel. In each branch, the 12 Ω and 6 Ω resistors are in series.

resistor-combination-equivalent-circuits-answer

For the top branch:

R1 = 12 + 6 = 18 Ω

For the bottom branch:

R2 = 12 + 6 = 18 Ω

Since R1 and R2 are in parallel:

\frac{1}{\mathrm{R}}=\frac{1}{\mathrm{R_1}}+\frac{1}{\mathrm{R_2}}

or, \frac{1}{\mathrm{R}}=\frac{1}{18}+\frac{1}{18}=\frac{2}{18}=\frac{1}{9}

Therefore, R = 9 Ω.

Hence, the resistance across AB when switch S is open is 9 Ω.

(b) When switch S is closed, the midpoints are connected. The circuit is rearranged into two parallel combinations connected in series.

resistor-combination-equivalent-circuits-answer

For the left combination containing 12 Ω and 6 Ω:

\frac{1}{\mathrm{R_1}}=\frac{1}{12}+\frac{1}{6}=\frac{1}{12}+\frac{2}{12}=\frac{3}{12}=\frac{1}{4}

Therefore, R1 = 4 Ω.

Similarly, for the right combination:

\frac{1}{\mathrm{R_2}}=\frac{1}{12}+\frac{1}{6}=\frac{1}{12}+\frac{2}{12}=\frac{3}{12}=\frac{1}{4}

Therefore, R2 = 4 Ω.

These two combinations are in series:

R = R1 + R2 = 4 + 4 = 8 Ω.

Hence, the resistance across AB when switch S is closed is 8 Ω.

Question 9 (i)

9 (i)Household CircuitsModerate3 Marks

An electric iron rated 1100 W, 220 V is operated for 5 hours. Calculate:

(a) the minimum rating of the fuse required.

(b) the energy consumed in kWh.

(c) the cost of the energy consumed, if the rate is ₹10 per unit.

Answer

Given, power (P) = 1100 W, voltage (V) = 220 V and time (t) = 5 h.

(a) Operating current = \frac{\text{P}}{\text{V}}  = \frac{1100}{220} = 5 A.

The fuse rating should be slightly higher than the operating current. Therefore, the minimum suitable fuse rating is 6 A.

(b) Energy consumed = Power × time

= 1100 × 5

= 5500 Wh = 5.5 kWh.

(c) Cost of energy consumption = 5.5 × ₹ 10 = ₹ 55.

Question 9 (ii)

9 (ii)Electro-magnetismModerate3 Marks

When the magnet shown in the diagram is moved towards the coil at a speed of 5 m s−1, the galvanometer shows a certain deflection to the right.

magnet-moving-towards-coil-galvanometer

How will the direction and magnitude of deflection change when the coil also moves with a speed of 5 m s−1:

(a) in the direction of motion of the magnet?

(b) in the opposite direction to the motion of the magnet?

Answer

The galvanometer deflection depends on the rate of change of magnetic flux and hence on the relative motion between the magnet and coil.

(a) The magnet and coil move in the same direction at the same speed, so there is no relative motion. No current is induced and the galvanometer shows no deflection.

(b) The magnet and coil move in opposite directions, so their relative speed is 10 m s−1. The direction of deflection remains to the right, but its magnitude increases.

Question 9 (iii)

9 (iii)RadioactivityModerate4 Marks

(a) (i) Which element is used in the lining of the special aprons worn by workers in nuclear power plants?

(ii) Why is this element preferred?

(b) 2411Na emits a nuclear radiation which does not alter the mass number but is deflected by a magnetic field.

  1. Name the type of nuclear radiation emitted by 2411Na.
  2. Write the equation for this radioactive decay.
Answer

(a) (i) Lead is used in the lining of the special aprons.

(ii) It is preferred because it is a dense metal and absorbs harmful nuclear radiations effectively.

(b) (1) The emitted radiation is beta (β) radiation.

(2) Radioactive decay equation:

{}^{24}_{11}\mathrm{Na}\longrightarrow{}^{24}_{12}\mathrm{Mg}+{}^{0}_{-1}\text{β}

In beta decay, the atomic number increases by 1 while the mass number remains unchanged.