**XII – ISC Board 2018**

**P****hysical Science**

**SECTION – A**

**Question 1 **

**(A) Choose the correct alternative (a), (b), (c) or (d) for each of the questions.**

**(i) The order of coloured rings in a carbon resistor is red, yellow, blue and silver. The resistance of the carbon resistor is:**

**(a) 24 x 10 ^{6 }Ω ± 5%**

**(b) 24 x 10 ^{6 }Ω ± 10%**

**(c) 34 x 10 ^{4 }Ω ± 10%**

**(d) 26 x 10 ^{4 }Ω ± 5%**

**Solution**

**Explanation: **

**(ii) A circular coil carrying a current I has radius R and number of turns N. If all the three, i.e. the current I, radius R and number of turns N are doubled, then, magnetic field at its centre becomes:**

**(a) Double **

**(b) Half **

**(c) Four times **

**(d) One fourth**

**Solution**

**Explanation: **

**(iii) An object is kept on the principal axis of a concave mirror of focal length 10 cm. at a distance of 15 cm from its pole. The image formed by the mirror is:**

**(a) Virtual and magnified **

**(b) Virtual and diminished**

**(c) Real and magnified **

**(d) Real and diminished**

**Solution**

**Explanation: **

**(iv) Einstein’s photoelectric equation is:**

**(a) E _{max }= hλ – ϕ_{0}**

**(b) E _{max }= {hc \over λ} – ϕ_{0}**

**(c) E _{max }= hv + ϕ_{0}**

**(d) E _{max }= {hv \over λ} + ϕ_{0}**

**Solution**

**Explanation: **

**(v) In Bohr’s model of hydrogen atom, radius of the first orbit of an electron is r0 . Then, radius of the third orbit is:**

**(a) {r_0 \over 9}**

**(b) r _{0}**

**(c) 3r _{0}**

**(d) 9r _{0}**

**Solution**

**Explanation: **

**(B) Answer the following questions briefly and to the point.**

**(i) In a potentiometer experiment, balancing length is found to be 120 cm for a cell E _{1} of emf 2V. What will be the balancing length for another cell E_{2} of emf 1.5V? (No other changes are made in the experiment.)**

**Solution**

**Explanation: **

**(ii) How will you convert a moving coil galvanometer into a voltmeter?**

**Solution**

**Explanation: **

**(iii) A moving charged particle q travelling along the positive x-axis enters a uniform magnetic field B. When will the force acting on q be maximum?**

**Solution**

**Explanation: **

**(iv) Why is the core of a transformer laminated?**

**Solution**

**Explanation: **

**(v) Ordinary (i.e. unpolarised) light is incident on the surface of a transparent material at the polarising angle. If it is partly reflected and partly refracted, what is the angle between the reflected and the refracted rays?**

**Solution**

**Explanation: **

**(vi) Define coherent sources of light.**

**Solution**

**Explanation: **

**(vii) Name a material which is used in making control rods in a nuclear reactor.**

**Solution**

**Explanation: **

**SECTION B **

**Question 2:**

**Define current density. Write an expression which connects current density with drift speed.**

**Solution**

**Explanation: **

**Question 3:**

**(a) A long horizontal wire P carries a current of 50A. It is rigidly fixed. Another wire Q is placed directly above and parallel to P, as shown in Figure 1 below. The weight per unit length of the wire Q is 0.025 Nm ^{-1} and it carries a current of 25A. Find the distance ‘r’ of the wire Q from the wire P so that the wire Q remains at rest.**

**OR **

**(b) Calculate force per unit length acting on the wire B due to the current flowing in the wire A.(See Figure 2 below)**

**Solution**

**Explanation: **

**Question 4:**

**(i) Explain Curie’s law for a paramagnetic substance.**

**(ii) A rectangular coil having 60 turns and area of 0.4m ^{2} is held at right angles to a uniform magnetic field of flux density 5 × 10^{–5}T. Calculate the magnetic flux passing through it.**

**Solution**

**Explanation: **

**Question 5: **

**What is motional emf ? State any two factors on which it depends.**

**Solution**

**Explanation: **

**Question 6:**

**(i) What is the ratio of the speed of gamma rays to that of radio waves in vacuum ?**

**(ii) Name an electromagnetic wave which is used in the radar system used in aircraft navigation.**

**Solution**

**Explanation: **

**Question 7:**

**A biconvex lens made of glass (refractive index 1.5) has two spherical surfaces having radii 20 cm and 30 cm. Calculate its focal length.**

**Solution**

**Explanation: **

**Question 8: **

**State any two difference between primary rainbow and secondary rainbow.**

**Solution**

**Explanation: **

**Question 9:**

**(i) State de Broglie hypothesis.**

**(ii) With reference to photoelectric effect, define threshold wavelength.**

**Solution**

**Explanation: **

**Question 10:**

**Calculate the minimum wavelength of the spectral line present in Balmer series of hydrogen.**

**Solution**

**Explanation: **

**Question 11:**

**(a) What is means by pair annihilation ? Write a balanced equation for the same.**

**OR **

**(b) What is meant by the terms half-life of a radioactive substance and binding energy of a nucleus ?**

**Solution**

**Explanation: **

**Question 12:**

**In a communication system, what is meant by modulation ? State any two types of modulation.**

**Section C **

*Answer all questions *

**Solution**

**Explanation: **

**Question 13:**

**Obtain an expression for intensity of electric field at a point in end on position, i.e., axial position of an electric dipole.**

**Solution**

**Explanation: **

**Question 14:**

**Deduce an expression for equivalent capacitance C when three capacitors C _{1} , C_{2} and C_{3 }connected in parallel.**

**Solution**

**Explanation: **

**Question 15:**

**(a) 𝜺 _{1} and 𝜺_{2} are two batteries having emf of 34V and 10V respectively and internal resistance of 1Ω and 2Ω respectively. They are connected as shown in figure below. Using Kirchhoff’s Laws of electrical networks, calculate the currents I_{1} and I_{2} .**

**(b) An electrical bulb is marked 200V, 100W. Calculate electrical resistance of its filament. If five such bulbs are connected in series to a 200V supply, how much current will flow through them ?**

**Solution**

**Explanation: **

**Question 16:**

**(a) For any prism, prove that :**

**‘n’ or µ = sin({A + \delta_m \over 2})\over sin({A \over 2})**

**where the terms have their usual meaning.**

**(b) When two thin lenses are kept in contact, prove that their combined or effective focal length F is given by :**

**{1\over F}={1\over f_1}+{1\over f_2}**

**where the terms have their usual meaning.**

**Solution**

**Explanation: **

**Question 17:**

**(i) In Young’s double slit experiment, show graphically how intensity of light varies with distance.**

**(ii) In Fraunhofer diffraction, how is the angular width of the central bright fringe affected when slit separation is increased?**

**Solution**

**Explanation: **

**Question 18:**

**Write one balanced equation each to show :**

**(i) Nuclear fission**

**(ii) Nuclear fusion**

**(iii) Emission of β- (i.e. a negative beta particle)**

**Solution**

**Explanation: **

**Question 19:**

**With reference to semi conductor devices, define a p – type semiconductor and a Zener diode. What is the use of Zener diode ?**

**Solution**

**Explanation: **

**Section D **

**Answer all questions **

**Question 20:**

**(a) An alternating emf of 220 V is applied to a circuit containing a resistor R having resistance of 160 Ω and a capacitor ‘C’ is series. The current is found to lead the supply voltage by an angle**

**θ = tan ^{-1} (3\4) .**

**(i) Calculate : **

**(1) The capacitive reactance**

**(2) Impedance of the circuit**

**(3) Current flowing in the circuit**

**(ii) If the frequency of the applied emf is 50 Hz, what is the value of the capacitance of the**

**capacitor ‘C’?**

**OR**

**(b) An A.C. generator generating an emf of 𝜺 = 300 sin (100 πt) V is connected to a series combination of 16 µ F capacitor, 1 H inductor and 100 Ω resistor..**

**Calculate :**

**(i) Impedence of the circuit at the given frequency.**

**(ii) Resonant frequency f _{0} .**

**(iii) Power factor at resonant frequency f _{0} .**

**Solution**

**Explanation: **

**Question 21:**

**(a) Draw a labelled ray diagram of an image formed by a refracting telescope with final image formed at inifity. Derive an expression for its magnifying power with the final image at infinity.**

**OR**

**(b) (i) Using Huygen’s wave theory, derive Snell’s law of refraction.**

**(ii) With the help of an experiment, state how will you identify whether a given beam of light is polarised or unpolarised.**

**Solution**

**Explanation: **

**Question 22:**

**(a) (i) The forward characteristic curve of a junction diode is shown in Figure 4 below :**

**Calculate the resistance of the diode at :**

**(1) V = 0.5 V**

**(2) I = 60 mA**

**(ii) Draw separate energy band diagram for conductors, semi-conductors and insulators and label each of them.**

**OR**

**(b) (i) The arrangement give below represents a logic gate :**

**Copy the following truth table in your answer booklet and complete it showing outputs at C**

**and D.**

**(ii) Draw a labelled diagram of a common emitter amplifier, showing waveforms of signal**

**voltage and output voltage.**

**Solution**

**Explanation: **