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ISC Class 12 Physics Solved Question Paper 2015

Short Answer Type

41.

Find the minimum wavelength of the emitted X-rays, when an X-ray tube is operated at 50 kV.

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42.

i) Define half-life of a radioactive substance.

ii) Using the equation, N = N_o e^{- $straight lambda$ t}, obtain the relation between half-life (T) and decay constant ( $straight lambda right parenthesis$ of a radioactive substance.

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43.

With the help of a suitable example and an equation, explain the term pair production.

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44.

Draw a labelled diagram of a full wave rectifier. Show how output voltage varies with time, if input voltage is a sinusoidal voltage.

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45.

What is a NAND gate? Write it's truth table?

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Long Answer Type

46.
Derive an expression for intensity of electric field at a point in broadside position or on an equatorial line of an electric dipole.

Electric field intensity at a point on the broad side-on position equatorial line:

Consider an electric dipole consisting of two equal but opposite charges -q and +q separated by a vector distance 2l.

Let P be a point at a distance r from the centre of the dipole O.

The electric intensity at P due to the dipole is the vector sum of the field due to the charge -q at A and +q at B.

The resultant intensity is the vector sum of E_A and E_B.

E_A and E_B can be resolved into two components.

The y-components of the field cancel each other because,

E_A sin

straight theta

= E_B sin

straight theta

, oppositely directed.
The x components add up to give the resultant field E.

Magnitude of E is,

open vertical bar straight E with rightwards harpoon with barb upwards on top close vertical bar space equals space E subscript A space cos space theta space plus space E B space cos space theta E space equals space fraction numerator 1 over denominator 4 pi epsilon subscript o end fraction. fraction numerator q over denominator open parentheses r squared plus l squared close parentheses end fraction cos space theta space plus space space space space space space space space space space fraction numerator 1 over denominator 4 pi epsilon subscript o end fraction. fraction numerator q over denominator open parentheses r squared plus l squared close parentheses end fraction cos space theta space space space space equals space 2 space straight x space fraction numerator 1 over denominator 4 pi epsilon subscript o end fraction fraction numerator q over denominator open parentheses r squared plus l squared close parentheses end fraction cos space theta

For the right angled triangle OPB,

cos space theta space equals space fraction numerator O B over denominator P B end fraction equals fraction numerator 1 over denominator left parenthesis r squared plus l squared right parenthesis to the power of bevelled 1 half end exponent end fraction

The dipole moment,

p = 2lq

E =

fraction numerator 1 over denominator 4 πε subscript straight o end fraction. space fraction numerator p over denominator left parenthesis r squared plus l squared right parenthesis to the power of bevelled 3 over 2 end exponent end fraction

E is directed along PC. The direction of E can be found out by drawing the line of force passing through the point P.

The direction of e at P is opposite to the direction of the dipole moment p.

That is, parallel to the line joining the two charges and directed from +q to -q.

When r>>1, then l² is very small as compared to r².

Then,

straight E subscript eq space equals space fraction numerator 1 over denominator 4 πε subscript straight o end fraction straight x straight p over open parentheses straight r squared close parentheses to the power of 3.2 end exponent space space space space space space space equals space fraction numerator 1 over denominator 4 πε subscript straight o end fraction straight x straight p over straight r cubed

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47.

Figure below shows a capacitor C, an inductor L and resistor R, connected in series to an ac supply of 220 V.

Calculate:

i) the resonant frequency of the given LCR circuit

ii) current flowing through the circuit

iii) Average power consumed by the circuit.

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48.

On the basis of Huygen's wave theory of light, show that the angle of reflection is equal to the angle of incidence. You must draw a labelled diagram for this deviation.

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