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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.

For infinite long line charge,

straight E space equals space fraction numerator straight lambda over denominator 2 πε subscript straight o straight r end fraction space equals space fraction numerator 2 straight lambda over denominator 4 πε subscript straight o straight r end fraction straight lambda space equals space linear space charge space density straight r space equals space distance

We have,

E = 9 x io⁴ N/C

r = 2 cm = 2 x 10^-2 m

Hence,

$9 space straight x space 10 to the power of 4 space equals space fraction numerator 2 space straight x space straight lambda space straight x space 9 space straight x space 10 to the power of 9 over denominator 2 space straight x space 10 to the power of negative 2 end exponent end fraction space space space space space space space space space space space straight lambda space equals space 10 to the power of 4 over 10 to the power of 11 space equals space 10 to the power of negative 7 space end exponent cm$

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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.

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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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