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ISC Class 12 Physics Solved Question Paper 2006

Short Answer Type

21. An infinite line charge produces a field of 9 x 10⁴ NC^-1 at a distance of 2 cm. Calculate the linear charge density.

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22. Derive the expression for the energy stored in a capacitor of capacitance C, charged to a potential V.

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23. A 100 W, 220 V bulb is connected to a 110 V dc source. Calculate the power consumed by the bulb.

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24. Derive an expression for the magnetic field at a point on the axis located at a distance ‘x’ from the centre of a magnetic dipole of length 21 and magnetic moment M.

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25.

An alternating emf of frequency 50 Hz is applied to a circuit with a resistor of 20 Ω, an inductor of 100 mH and a capacitor of 30 ηF connected in series.

(i) What is the angle by which the current leads or lags the applied emf ?

(ii) Represent the voltage and the current in a vector diagram showing the phase angle.

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26. PQ and MN are two parallel conductors at a distance I apart and connected by a resistance R as shown in figure 3. They are placed in a magnetic field B which is perpendicular to the plane of the conductors. A wire XY is placed over PQ and MN and then made to slide over PQ and MN with a velocity v.

Neglecting the resistance of PQ, MN and wire XY, calculate the work done per second to slide the wire XY.

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27. State Huygen’s principle in the wave theory of light. Using the principle, prove the laws of reflection of light.

Huygen’s Principle : Huygens gave a hypothesis for geometrical construction of the position of a common wave front at any instant, during the propagation of waves in a medium.

(i) Every point on the given wave front, called primary wave front, acts as a fresh source of new disturbance, called secondary waveless, which travel in all directions with the velocity of light in the medium.

(ii) A surface touching these secondary wavelets, tangentially in the forward direction at any instant gives the new wave front at that instant. This is called secondary wave front.

Reflection on the basis of wave theory :

According to Huygen’s principle, every print on AB is a source of secondary wavelets. Let the secondary wavelets from B strike. M₁ M₂ at A' in t seconds.

BA' = Ct ...(i)

where C is the velocity of light in the medium.

The secondary wavelets from A will travel the same distance C x t in the same time. Therefore, with A as a centre and C x t as radius, draw an arc B', so that,

AB' = Ct ...(ii)

For A'B' to be the reflected wave front, secondary wavelets starting from any other point D on the incident wave front AB must reach the corresponding point D' on A' B' after reflection at P, in exactly the same time as the secondary wavelets take to go from B to A.

For this, DP + PD' = BA' ...(iii)

To prove it, draw PN ⊥ BA'

DP = BN ...(iv)

In As. AA'B and AA'B'

AA' is common

∠ABA' = ∠AB'A' = 90° and BA' = AB' = Ct

Therefore As are congruent.

∴ ∠BAA' =

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28. A lamp placed 50 cm from a screen on one side produces the same illumination as a standard 25 cd lamp placed 100 cm away on the other side of the screen. What is the luminous intensity of the first lamp ?

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29. If ‘d’ is the distance covered by a light wave in air in ‘t’ seconds and D’ is the distance covered in a medium of refractive index ‘n in the same time, prove that, d = nD.

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30. Determine the angular separation between the central maximum and the first order maximum of the diffraction pattern due to a single slit of width 0.25 mm when light of wavelength 5890 A is incident on it normally.

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