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CBSE Class 12 Physics Solved Question Paper 2011

Short Answer Type

31.

State the law of radioactive decay.

Plot a graph showing the number (N) of undecayed nuclei as a function of time (t) for a given radioactive sample having half-life T_½.

Depict in the plot the number of undecayed nuclei at (i) t = 3 T_½ and (ii) t = 5 T_½.

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Long Answer Type

32.

(i) With the help of a labelled diagram, describe briefly the underlying principle and working of a step up transformer.

(ii) Write any two sources of energy loss in a transformer.

(iii) A step up transformer converts a low input voltage into a high output voltage.

Does it violate law of conservation of energy? Explain.

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33.
Derive an expression for the impedance of a series LCR circuit connected to an AC supply of variable frequency.

Plot a graph showing variation of current with the frequency of the applied voltage.

Explain briefly how the phenomenon of resonance in the circuit can be used in the
Tuning mechanism of a radio or a TV set.

a)

Expression for impedance in LCR series circuit:

Suppose a resistance R, inductance L and capacitance C are connected to series and an alternating voltage V = is applied across it.

Since L, C and R are connected in series, current flowing through them is the same. The voltage across R is V_R, inductance across L is V_L and across capacitance is V_C.The voltage V_R and current i are in the same phase, the voltage V_L will lead the current by angle 90° while the voltage V_C will lag behind the current by 90°.

Clearly V_Cand V_L are in opposite directions, therefore their resultant potential difference =V_C -V_L(if V_C >V_C).

Thus, V_R and (V_C -V_L) are mutually perpendicular and the phase difference between them is 90°. As seen in the fig, we can say that, as applied voltage across the circuit is V, the resultant of V_R and (V_C -V_L) will also be V.

So,

Therefore, Impedance of the circuit is given by,

This is the impedence of the LCR series circuit.

b)

The below graph shows the variation of current with the frequency of the applied voltage.

c)

A radio or a TV set has a L-C circuit with capacitor of variable capacitance C. The circuit remains connected with an aerial coil through the phenomenon of mutual inductance. Suppose a radio or TV station is transmitted a programme at frequency f, then waves produce alternating voltage of frequency f, in area, due to which an emf of same frequency is induced in LC circuit, When capacitor C is in circuit is varied then for a particular value of capacitance, , the resonance occurs and maximum current flows in the circuit; so the radio or TV gets tuned.

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34.

(a) Draw a ray diagram to show refraction of a ray of monochromatic light passing through a glass prism.

Deduce the expression for the refractive index of glass in terms of angle of prism and angle of minimum deviation.

(b) Explain briefly how the phenomenon of total internal reflection is used in fiber optics.

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35.

(a) Obtain lens makers formula using the expression

$n subscript 2 over v minus n subscript 1 over u equals fraction numerator left parenthesis n subscript 2 minus n subscript 1 right parenthesis over denominator R end fraction$

Here the ray of light propagating from a rarer medium of refractive index (n₁) to a denser medium of refractive index (n₂) is incident on the convex side of spherical refracting surface of radius of curvature R.

(b) Draw a ray diagram to show the image formation by a concave mirror when the object is kept between its focus and the pole. Using this diagram, derive the magnification formula for the image formed.

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