Class-12-Physics-Question-Paper-2078-Board-Exam-PDF
Group 'A' 11 x 1 = 11
Rewrite the correct options of each questions in your answer sheet.
1. In rotational motion, the physical quantity that imparts angular acceleration is,
(A) Force
(B)Torque
(C) Moment of inertia
(D) Angular momentum
Answer = (B) Torque imparts angular acceleration in rotational motion.
2. Two identical springs die arranged with a black as in figure. The oscillation
frequency of the mass is 'f’. If one spring is removed, the frequency of the
Oscillation will be.
(A) f
(B)2f
(C)√2f
(D) 7/√2f
Answer = (B) 2f
When two identical springs are arranged with a block as in the figure, the frequency of oscillation is given by f = 1 / (2π) * √(k / m), where k is the spring constant and m is the mass of the block.
If one spring is removed, the effective spring constant is halved and the frequency of oscillation becomes f = 1 / (2π) * √(k / 2m), which is equal to 2f.
3. A liquid does not wet the surface of a solid if the angle of contact is,
(A) 90°
(B) less than 90°
(C) Greater than 90°
(D) 0°
Answer = (A) 90°
A liquid does not wet the surface of a solid if the angle of contact between the liquid and the solid is 90°. This means that the liquid forms a droplet on the solid surface and does not spread out. The angle of contact is determined by the relative values of the forces of adhesion (the force that attracts the liquid to the solid) and the forces of cohesion (the forces that hold the liquid molecules together). If the forces of adhesion are weaker than the forces of cohesion, the angle of contact is greater than 90° and the liquid will not wet the surface.
4. Identify the wrong statement
(A) for isothermal process, ∆T=0
(B) for isochoric process, ∆V= 0
(C) for isobaric process, ∆P=0
(D) for cyclic process, ∆W: 0
Answer = (P) for cyclic process, ∆W = 0
This statement is incorrect. In a cyclic process, the total work done by the system (∆W) is not necessarily equal to zero. It depends on the specific process and the initial and final states of the system. For example, in a thermodynamic cycle, the work done by the system can be positive, negative, or zero, depending on the specific path followed by the system and the pressure-volume changes that occur during the cycle.
5.The maximum efficiency an engine operating between 30°C and 300°C is.
(A) 4.71%
(B) 47%
(C) 90%
(D) 9%
Answer = (A) 4.71%
The maximum efficiency of an engine operating between two temperatures T1 and T2 is given by the Carnot efficiency, which is defined as:
η = 1 - T2 / T1
In this case, T1 = 30 + 273.15 = 303.15 K and T2 = 300 + 273.15 = 573.15 K, so the Carnot efficiency is:
η = 1 - T2 / T1 = 1 - 573.15 / 303.15 = 1 - 1.898 = -0.898 = -89.8% = 4.71% (rounded to two decimal places)
So, the maximum efficiency of the engine is 4.71%.
6.In which frequency range the infrasonic wave lies?
(A) (10-20)Hz
(B) (30-40)Hz
(C) (20-30)Hz
(D) (50-60)Hz
Answer = (A) (0-20)Hz
Infrasonic waves are sound waves with a frequency lower than 20 Hz. They are usually not audible to human ears, but can be felt as vibrations and can have significant impacts on the environment. These low-frequency sound waves can be produced by natural phenomena such as earthquakes, volcanic eruptions, and ocean waves, as well as by man-made sources such as industrial processes and explosions. The frequency range of infrasonic waves is typically defined as 0 to 20 Hz.
7. In Fraunhofer diffraction, the incident wave front should be,
(A) elliptical
(B) plane
(C) spherical
(D) cylindrical
Answer = (B) Plane
In Fraunhofer diffraction, a plane wave front incident on a rectangular aperture or a diffraction grating produces diffracted waves that form a diffraction pattern on a distant screen. The diffracted waves form an interference pattern with well-defined peaks and troughs. The incident wave front must be plane in order to produce this well-defined diffraction pattern. An elliptical or spherical wave front would produce a more complex pattern with less distinct peaks and troughs.
8. If specific resistance of a potentiometer wire is 10-7Ωm, current flowing
through it is 0.1A and cross sectional area of wire is 10-6 m², then potential
gradient will be.
(A) 10-2V/m
(B) 10-4 V/m
(C) 10-6 V/m
(D) 10-8V/m
Answer = (A) 10-2 V/m
The potential gradient (V/m) of a wire is given by:
V/m = V / L = IR / L
Where V is the potential difference across the wire, I is the current flowing through the wire, R is the resistance of the wire, and L is the length of the wire. The resistance of a wire is given by:
R = ρL / A
Where ρ is the specific resistance of the wire and A is the cross-sectional area of the wire. Substituting this into the expression for V/m and solving for V/m, we get:
V/m = IR / L = I * ρL / A * L = I * ρ / A
Given specific resistance of the wire is 10-7 Ωm, current flowing through the wire is 0.1 A, and cross-sectional area of the wire is 10-6 m², we get:
V/m = I * ρ / A = 0.1 * 10-7 / 10-6 = 10-2 V/m
So, the potential gradient is 10-2 V/m.
9. A coil having N-number of turns and cross-section area A carries a current
1. The quantity NIA is.
(A) magnetic flux
(B) magnetic field
(C) magnetic susceptibility
(D) magnetic moment
Answer = (D) Magnetic moment
The magnetic moment of a coil is proportional to the product of the number of turns (N), the current (I), and the cross-sectional area (A) of the coil. It is represented by the symbol μ and is a measure of the strength and direction of the magnetic field generated by the coil. The magnetic moment is proportional to the magnetic flux passing through the coil, but it is not the same as the magnetic flux itself. The magnetic moment is a vector quantity and can be used to calculate the torque experienced by the coil in a magnetic field.
10. At resonance, in series LCR circuit, which relation does not hold good,
(A) ⩊=1/√Lc
(B) L⩊=1/C⩊
(C) C⩊=1/ L⩊
(D) ⩊=1/Lc
Answer = (B) L⩊=1/C⩊
At resonance in a series LCR circuit, the following relations hold good:
⩊ = 1/√Lc
C⩊ = 1/⩊L
Where ⩊ is the resonant angular frequency, L is the inductance, and C is the capacitance. The above two equations are derived from the characteristic equation of the series LCR circuit, and they represent the resonant conditions for the circuit.
However, the relation L⩊=1/C⩊ does not hold good at resonance, as it is not a derived equation but a combination of the two derived equations. So, the correct answer is (B) L⩊=1/C⩊.
11. Which of the following one is correct?
(A) E²=P²C
(B)E²=P²C²
(C) E²=PC²
(D) E²=P²/C²
Answer = (A) E² = P²C
The equation E² = P²C is the well-known equation for electromagnetic waves and is known as the wave equation. It relates the energy (E) carried by an electromagnetic wave to its power (P) and the velocity of light (C). The equation states that the energy carried by the wave is proportional to the square of its power and inversely proportional to the square of its velocity. This equation is important for understanding the behavior of electromagnetic waves and for calculating the energy and power of these waves in various applications.
Group 'B'
8x5=40
12)The angular speed is inversely proportional to the moment of inertia, that is given by the principal of conservation of energy.
a) In a flywheel most of the mass is concentrated at the rim? Explain why? 1
Answer = The angular speed of a rotating body is inversely proportional to its moment of inertia. The moment of inertia of a body depends on the distribution of mass within the body. In a flywheel, most of the mass is concentrated at the rim so that the moment of inertia is minimized, which in turn maximizes the angular speed for a given amount of energy. This helps to ensure that the flywheel rotates with as much stability and uniformity as possible.
b) The angular velocity of the earth around the sun increases, when it comes closer to the sun. Why? 2
Answer = The angular velocity of the Earth around the Sun does not actually increase when it comes closer to the Sun. According to the laws of Keplerian motion, the closer an object is to the Sun, the faster it moves in its orbit. However, this increase in speed is due to the decrease in the semi-major axis of the elliptical orbit, not an increase in angular velocity.
c) If the earth were to shrink suddenly, what would happen to the length of the day? 2
Answer = If the Earth were to shrink suddenly, its moment of inertia would decrease and its angular velocity would increase. As a result, the length of a day (the time it takes for the Earth to make one complete rotation) would decrease. This would result in a faster rotation and shorter days.
13) Simple harmonic motion is defined from periodic functions like sine or cosine closer to the sun. Why?
Answer =
a) State the basic equation of motion for a body executing simple harmonic motion. 1
Answer = The basic equation of motion for a body executing simple harmonic motion is given by:
x(t) = A cos(ωt + φ)
where x(t) is the displacement at time t, A is the amplitude of the motion, ω is the angular frequency, and φ is the phase angle.
b) Find expression for velocity and acceleration of a particle describing SHM. 2
Answer = The velocity and acceleration of a particle describing simple harmonic motion can be found by taking the first and second derivatives of the displacement equation, respectively:
v(t) = dx(t)/dt = -Aω sin(ωt + φ)
a(t) = dv(t)/dt = -Aω^2 cos(ωt + φ)
c) The tip of turning fork goes through 550 complete vibrations in 1 sec. Find the angular frequency and time period of the motion. 1+1=2
Answer = Given that the tip of the tuning fork goes through 550 complete vibrations in 1 second, the frequency of the motion is 550 vibrations per second, or 550 Hz. The angular frequency can be found from the relationship ω = 2πf, giving:
ω = 2πf = 2π * 550 Hz = 3467 rad/s
The time period T is the time for one complete vibration, and can be found from the relationship T = 1/f, giving:
T = 1/f = 1 / 550 Hz = 1.82 x 10^-3 s
OR
a) Define surface tension 1
Answer = Surface tension is a property of liquids that results from the attraction between the molecules at the surface of the liquid and the molecules within the bulk of the liquid. It causes the surface of the liquid to act like an elastic membrane and resist an external force, resulting in a characteristic curvature of the surface known as surface tension.
b) State Bernoulli's theorem. 1
Answer = Bernoulli's theorem is a principle in fluid dynamics that states that for an inviscid flow (a flow in which there is no friction or viscosity), an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.
c) Castor oil at 20°C has a coefficient of viscosity 2.42 Nsm2 and density 940 kgm3.Calculate the terminal velocity of a steel ball of radius 2mm falling under the gravity in the oil, taking the density of steel as 7800kg/m3(g=10m/s2) 3
Answer = To calculate the terminal velocity of a steel ball of radius 2mm falling through castor oil at 20°C, we can use the equation for terminal velocity in a viscous fluid:
v_t = sqrt((2mg) / (ρ_s C_d ρ))
where m is the mass of the steel ball, g is the acceleration due to gravity, ρ_s is the density of the steel, C_d is the drag coefficient (approximately 0.47 for a sphere), ρ is the density of the oil, and μ is the viscosity of the oil.
The mass of the steel ball can be calculated as follows:
m = (4/3) π (0.002 m)^3 * 7800 kg/m^3 = 3.87 x 10^-9 kg
Substituting the values into the equation, we get:
v_t = sqrt((2 * 3.87 x 10^-9 kg * 10 m/s^2) / (0.47 * 940 kg/m^3 * 2.42 Ns/m^2)) = 0.044 m/s
So the terminal velocity of the steel ball in the castor oil at 20°C is 0.044 m/s.
14. Adiabatic process 1
Answer = Adiabatic process is a process in thermodynamics where there is no heat transfer between the system and its surroundings.
a) Define a diabetic process in thermodynamics. 3
Answer = A adiabatic process in thermodynamics is a process in which no heat is added or removed from the system. This means that the internal energy of the system remains constant during the process, and any changes in temperature are due solely to the work done on or by the system. An adiabatic process can be thought of as a process that is isolated from its surroundings and no heat is exchanged between the system and the surroundings.
b) Derive expression for work done during adiabatic process. 1
Answer = The work done during an adiabatic process can be expressed using the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system:
dU = Q - W
In an adiabatic process, Q = 0, so the work done by the system can be expressed as:
W = -dU
c) Write the mathematical expression of entropy. 1
Answer = The mathematical expression of entropy is given by:
S = k * ln(Ω)
where S is the entropy, k is the Boltzmann constant, and Ω is the number of microstates available to the system. The entropy is a measure of the disorder or randomness of a system, and its increase over time is known as the second law of thermodynamics.
15. a) Define an organ pipe. 1
Answer = An organ pipe is a cylindrical or rectangular tube used to produce sound in a musical instrument, such as an organ or a pipe organ. The sound is produced by the vibration of air within the pipe.
b) Describe the various modes of vibration of the air column in a closed organ pipe. 3
Answer = There are three modes of vibration of the air column in a closed organ pipe:
- Fundamental mode: This is the lowest frequency at which the air column vibrates, and it determines the pitch of the sound produced.
- First overtone: This is the second harmonic of the air column, with a frequency that is twice that of the fundamental mode.
- Second overtone: This is the third harmonic of the air column, with a frequency that is three times that of the fundamental mode.
c) What is end correction? 1
Answer = End correction is a correction factor that is applied to the length of an organ pipe to account for the effect of the pipe ends on the vibration of the air column. The length of an organ pipe is typically corrected so that the pipe will produce the desired pitch when it is played.
OR
a) State Doppler's effect. 1
Answer = Doppler's effect, also known as the Doppler shift, is a phenomenon that occurs when a source of sound or a moving object is approaching or receding from an observer. The effect is characterized by a change in the frequency and wavelength of the sound or light waves as they travel towards or away from the observer.
b) Derive the apparent frequency of sound when an observer moves towards a stationary source. 2
Answer = The apparent frequency of sound when an observer moves towards a stationary source can be derived as follows:
Let the speed of sound be v, the frequency of the sound wave emitted by the source be f, and the relative velocity of the observer be v_r. Then, the apparent frequency of the sound wave as perceived by the observer is given by:
f' = f * (v + v_r) / v
where f' is the apparent frequency, and v_r is the relative velocity of the observer towards the source (positive if the observer is moving towards the source and negative if the observer is moving away from the source).
c)A stationary motion detector sends sound waves of 150 KHz towards a
truck approaching at a speed of 120km/hr. What is the frequency of wave
reflected back to detector? (Velocity of sound in air =340m/s) 2
Answer = The frequency of the wave reflected back to the motion detector can be calculated as follows:
Let v_o be the velocity of the truck approaching the motion detector, and v_s be the velocity of sound in air. The relative velocity of the truck with respect to the sound wave is given by:
v_r = v_o - v_s
The frequency of the wave reflected back to the detector is then given by:
f' = f * (v_s - v_r) / v_s = f * (v_s - (v_o - v_s)) / v_s = f * (2 * v_s - v_o) / v_s
Plugging in the values, we get: v_s = 340 m/s v_o = 120 km/hr = 33,000 m/hr = 33,000 / 3600 m/s = 9.17 m/s f = 150 KHz = 150,000 Hz
f' = 150,000 * (2 * 340 - 9.17) / 340 = 150,000 * (680 - 9.17) / 340 = 150,000 * 670.83 / 340 = 150,000 * 1.97 = 297,000 Hz
16. a)Differentiate See beak's effect and Peltier's effect. 2
Answer = Seebeck effect and Peltier effect are both thermoelectric effects that describe the relationships between heat, electricity, and temperature.
The Seebeck effect, also known as the thermoelectric effect, is the phenomenon in which a voltage is generated between two ends of a material when a temperature gradient is applied across the material. This effect is used in thermoelectric generators to convert heat into electricity.
The Peltier effect, on the other hand, is the phenomenon in which an electric current flowing through a material causes a change in temperature at the two ends of the material. This effect is used in thermoelectric cooling devices to remove heat from a system.
In summary, the Seebeck effect describes the conversion of temperature differences into electrical voltage, while the Peltier effect describes the conversion of electrical energy into thermal energy.
b)Explain the variation of thermo-emf with temperature. 3
Answer = The variation of thermo-emf with temperature can be described as follows:
Thermo-emf, also known as the Seebeck voltage, is the voltage generated by the Seebeck effect. The magnitude of the thermo-emf depends on the temperature difference across the material and the properties of the material itself.
In general, the thermo-emf is proportional to the temperature difference and the material's Seebeck coefficient, which is a material-specific constant that describes the magnitude of the voltage generated per unit temperature difference.
The relationship between thermo-emf and temperature can be expressed as:
E = S * ΔT
where E is the thermo-emf, S is the Seebeck coefficient, and ΔT is the temperature difference.
The Seebeck coefficient can also depend on temperature, and its variation with temperature can be described by the material's temperature dependence of the Seebeck coefficient, which is another material-specific constant. The temperature dependence of the Seebeck coefficient can be used to predict the behavior of the thermo-emf as a function of temperature.
17) When a charge particle moves in a uniform magnetic field, it experiences a force called the Lorentz force? 1
Answer = The vector representation of the Lorentz force can be represented as:
F = q * (v x B)
where F is the Lorentz force, q is the charge of the particle, v is the velocity of the particle, and B is the magnetic field.
a) What is the vector representation of Lorentz force? 1
Answer =
b) State Fleming left hand rule. 1
Answer = Fleming's Left-Hand Rule is a mnemonic used to describe the relationship between the direction of the current, the magnetic field, and the force experienced by a moving charge. According to this rule, if the thumb of the left hand points in the direction of the current, the index finger points in the direction of the magnetic field, and the middle finger points in the direction of the force experienced by the moving charge.
c) A horizontal straight wire 5 cm long weighing 1.2gm1 is placed
perpendicular to a uniform horizontal magnetic field of flux density
0.6T. If the resistance of the wire is 3.82 Ωm1, calculate the p.d. that
has to be applied between the ends of the wire to make it just
self-supporting. 3
Answer = To calculate the p.d. that has to be applied between the ends of the wire to make it just self-supporting:
The Lorentz force experienced by a moving charge in a magnetic field can be used to calculate the force experienced by a current-carrying wire in a magnetic field. The force experienced by the wire is proportional to the current in the wire and the magnetic field.
The force experienced by the wire is given by:
F = B * I * L
where F is the force, B is the magnetic field, I is the current in the wire, and L is the length of the wire.
In this case, the length of the wire is 5 cm, the magnetic field is 0.6 T, and the resistance of the wire is 3.82 Ω/m. The current in the wire can be calculated using Ohm's law:
I = V / R
where V is the p.d. applied between the ends of the wire and R is the resistance of the wire.
The force experienced by the wire must be equal to the weight of the wire, which is 1.2 g, to make the wire self-supporting. Therefore, we can set the two equal and solve for V:
1.2 g = B * I * L 1.2 g = 0.6 T * (V / 3.82 Ω/m) * 0.05 m V = (1.2 g * 3.82 Ω/m) / (0.6 T * 0.05 m)
V = 1.46 V
The p.d. that has to be applied between the ends of the wire to make it just self-supporting is 1.46 V.
18. Electron is deviated in electric and magnetic fields.
a) What path does the electron follow in electric field when the electron
is projected normally in the field ? 1
Answer = When an electron is projected normally in an electric field, it follows a parabolic path. The electric field exerts a force on the electron that accelerates it along the direction of the field.
b) An electron passes through a space without deviation. Does it mean,
there is no fields? 2
Answer = No, it does not necessarily mean that there is no field. An electron passing through a space without deviation could mean that the electric and magnetic fields it is passing through are uniform and cancel each other out. Alternatively, it could mean that the electric and magnetic fields are not strong enough to cause significant deviation.
c) Is there any condition that an electron does not experience any force
inside the magnetic field? 2
Answer = Yes, there is a condition where an electron does not experience any force inside a magnetic field. This occurs when the velocity of the electron is perpendicular to the magnetic field, such that the magnetic field exerts no force on the electron. The direction of the velocity of the electron remains unchanged in this case, but the velocity itself may change due to other forces such as electric fields.
19. What is rectification? 1
Answer = Rectification is the process of converting alternating current (AC) into direct current (DC).
b) Explain rectifier circuit operation with two diodes. 3
Answer = A rectifier circuit using two diodes operates by allowing current to flow through one diode in one direction during each half cycle of the AC input. The output of the rectifier circuit is a pulsed DC waveform. During the positive half-cycle of the AC input, one diode is forward-biased and conducts current, while the other diode is reverse-biased and does not conduct. During the negative half-cycle, the forward and reverse bias conditions are reversed, so that the current flows through the other diode. The output of the rectifier circuit is smoothed using a filter to produce a steady DC voltage.
c) What happens when one of the diode becomes functionless? 1
Answer = If one of the diodes in a rectifier circuit becomes functionless, the rectifier circuit will no longer produce a pulsed DC waveform, and the output will be greatly reduced. The presence of a functionless diode could cause the rectifier circuit to behave as a half-wave rectifier instead of a full-wave rectifier, which would result in a greatly reduced DC output voltage. The rectifier circuit may also be unable to rectify the AC input correctly, leading to a distorted DC output waveform.
Group 'C' 8x3=24
20. a) Write sustainable conditions for interference? 2
Answer = The following conditions must be met for interference to occur:
- The waves must have the same wavelength and frequency.
- The waves must be coherent, meaning they must have a constant phase relationship.
b)"The bright and dark fringes are equally spaced." Justify this statement
from Young's double slit experiment. 3
Answer = The statement "the bright and dark fringes are equally spaced" can be justified by considering the interference pattern produced by Young's double slit experiment. In this experiment, light passing through two parallel slits interferes to produce a series of bright and dark fringes on a screen behind the slits. The distance between consecutive bright fringes (or consecutive dark fringes) is equal, as is the distance between a bright and a dark fringe. This is because the distance between the fringes is directly proportional to the wavelength of the light used in the experiment.
c) In a Young's slits experiment the separation of first to fifth fringes is
2.5 mm when the wave length used is 620 cm. The distance from the
slits to the screen is 80 cm. Calculate the separation of two slits. 3
Answer = The separation of the two slits in Young's double slit experiment can be calculated using the following formula:
d = λL/a,
where d is the separation of the two slits, λ is the wavelength of light used in the experiment, L is the distance from the slits to the screen, and a is the separation of the first to fifth fringes.
Substituting the given values, we have:
d = 620 cm × 80 cm / 2.5 mm = 6.2 × 10^6 / 0.025 = 248 × 10^6 mm = 248 meters.
21. Kirchhoff's laws in electricity are very useful in solving the complicated
circuit connections.
a) What is the significance of first law ? 1
Answer = The first law of Kirchhoff, also known as Kirchhoff's law of conservation of charge, states that the total charge in a closed circuit must remain constant, meaning the total current entering a node in a circuit must equal the total current leaving that node. This law is based on the principle of conservation of charge, which states that electric charge cannot be created or destroyed, only transferred from one place to another.
b) State and explain second law with circuit diagram. 2
Answer = The second law of Kirchhoff, also known as Kirchhoff's law of conservation of energy, states that the total energy in a circuit must remain constant. This law is based on the principle of conservation of energy, which states that energy cannot be created or destroyed, only converted from one form to another. The second law can be applied to electric circuits by considering the potential difference (voltage) across each element in the circuit, such as a resistor, battery, or capacitor. The total voltage around any closed loop in the circuit must be equal to zero, meaning the sum of the voltages across all the elements in the loop must be equal to zero.
circuit diagram
c) Apply these laws calculate unknown value of resistance. 3
Answer = To apply Kirchhoff's laws to calculate the unknown value of resistance in a circuit, we can set up a system of equations based on the voltages and currents in the circuit. For example, if there are N nodes in a circuit, we can write N equations based on Kirchhoff's first law (conservation of charge) and another N-1 equations based on Kirchhoff's second law (conservation of energy). Then, we can use these equations to solve for the unknown voltages, currents, and resistances in the circuit.
d) What is meter bridge ? Write name of material used to construct meter
bridge. 1+1=2
Answer = A meter bridge is a laboratory instrument used to measure resistance. It consists of a long wire of known resistance, usually made of Nichrome or other conductive material, that is used to balance a circuit. The meter bridge is typically used in conjunction with a potentiometer, which is an instrument that measures the potential difference (voltage) across a circuit element. By measuring the potential difference and current in the circuit, and using Ohm's law (V = IR), the resistance of an unknown element can be calculated.
OR
a) Derive the expression for impedance in L-C-R circuit. 3
Answer = The impedance of an L-C-R circuit can be derived using the equation Z = √(R^2 + (X_L - X_C)^2), where R is the resistance, X_L is the reactance of the inductor, and X_C is the reactance of the capacitor. Reactance is a measure of the opposition of a component to the flow of alternating current and is given by X = 2πfL for inductors and X = 1/(2πfC) for capacitors, where f is the frequency of the alternating current.
b) Find the condition of resonance L-C-R circuit. 2
Answer = The condition of resonance in an L-C-R circuit occurs when X_L = X_C. At this condition, the impedance of the circuit is equal to R, and the current in the circuit is at a maximum. This is because the energy stored in the inductor and capacitor is alternately transferred to each other, resulting in maximum energy transfer to the load resistance R.
c) A circuit consists of a capacitor of 2µF and a resistor of 1000Ω. An
alternating emf of 12V (rms) and frequency 50 Hz is applied. Find the
current flowing, the voltage across capacitor and the phase angle
between the applied emf and current. 3
Answer = To find the current flowing in the circuit, we can use the formula for impedance, Z = √(R^2 + (X_c - X_L)^2), where R is the resistance, X_c is the capacitive reactance, and X_L is the inductive reactance. Since there is no inductor in the circuit, X_L is equal to zero.
The capacitive reactance can be found using the formula X_c = 1/(2 * pi * f * C), where f is the frequency (50 Hz) and C is the capacitance (2 µF).
With these values, we can calculate the impedance: Z = √(1000^2 + (1/(2 * pi * 50 * 2 * 10^-6))^2) = 1000 Ω.
The current flowing in the circuit can then be found using Ohm's law, I = V/Z, where V is the rms voltage (12 V).
I = 12/1000 = 0.012 A.
The voltage across the capacitor can be found using the formula V_c = I * X_c = 0.012 * (1/(2 * pi * 50 * 2 * 10^-6)) = 0.746 V.
The phase angle between the applied emf and the current can be found using the formula tanΦ = X_c/R = (1/(2 * pi * 50 * 2 * 10^-6))/1000 = 4.44 * 10^-5 radians.
So, the current flowing in the circuit is 0.012 A, the voltage across the capacitor is 0.746 V, and the phase angle between the applied emf and the current is 4.44 * 10^-5 radians.
22.) State Bohr's postulate of atomic model. 2
Answer = Bohr's postulate of atomic model is a theory that explains the behavior of electrons in atoms. It states that electrons orbit the nucleus of an atom in specific, stable orbits, and that the electrons can only occupy these orbits and not any other intermediate positions. The postulate also states that the electrons can only jump from one orbit to another through the emission or absorption of a quantum of energy.
b) Derive an expression for radius of nth orbit in H-atom. 3
Answer = The expression for the radius of the nth orbit in the Hydrogen atom (Bohr model) can be derived using the following formula:
rn = 0.529 x 10^-10 m * n^2
where rn is the radius of the nth orbit, n is the principal quantum number and 0.529 x 10^-10 m is the Bohr radius, which is a constant.
This formula can be derived from the equation for the potential energy of the electron in the Hydrogen atom:
En = -(e^2 / (4 * pi * ε0)) * (1 / n^2)
where e is the electron charge, ε0 is the electric constant and n is the principal quantum number. The formula for the kinetic energy of the electron can be derived from the Heisenberg Uncertainty Principle:
T = (h^2 / (8 * pi^2 * m)) * (1 / n^2)
where h is Planck's constant, m is the mass of the electron and n is the principal quantum number.
Equating the kinetic and potential energy, we get:
(e^2 / (4 * pi * ε0)) * (1 / n^2) = (h^2 / (8 * pi^2 * m)) * (1 / n^2)
Solving for n^2, we get:
n^2 = (m * e^2) / (4 * pi * ε0 * h^2)
Using the value of the Bohr radius, we get the expression for the radius of the nth orbit in the Hydrogen atom:
rn = 0.529 x 10^-10 m * n^2
c) Calculate de Brogle wavelength of electron when it is accelerated by
500 volt. ( mass of electron 9.1x10-31 kg, Planck's constant
6.62x10-34Js, charge of electron 1.6x10-19C) 3
Answer = The de Broglie wavelength of a particle is given by the equation:
λ = h / (mv)
where h is Planck's constant (6.62 x 10^-34 Js), m is the mass of the particle (9.1 x 10^-31 kg), and v is its velocity (v = eU / m, where e is the charge of the electron (1.6 x 10^-19 C) and U is the voltage applied to the electron (500 V)).
Substituting the given values, we get:
λ = (6.62 x 10^-34 Js) / [(9.1 x 10^-31 kg) (eU / m)]
λ = (6.62 x 10^-34 Js) / [(9.1 x 10^-31 kg) (1.6 x 10^-19 C) (500 V) / (9.1 x 10^-31 kg)]
λ = 6.62 x 10^-34 Js / (1.6 x 10^-19 C x 500 V)
λ = 6.62 x 10^-34 Js / (8 x 10^-17 J)
λ = 8.27 x 10^-18 m
Therefore, the de Broglie wavelength of the electron when it is accelerated by 500 volts is 8.27 x 10^-18 meters.
OR
Radio activity is the spontaneously occurring phenomenon in nature.
a) What is radio activity? 1
Answer = Radioactivity is the process by which atomic nuclei spontaneously emit particles and energy, causing them to become more stable. It is a property of certain isotopes of elements that emit alpha, beta, or gamma rays, which are high-energy photons or particles that can penetrate matter. This emission of particles and energy changes the atomic nucleus into a different nucleus, releasing energy in the process.
b) Obtain N= N0e-λt in radio active decay law. 3
Answer = The radioactive decay law states that the number of radioactive atoms (N) decreases over time, and is given by the expression:
N = N0 * e^(-λt)
where:
- N0 is the initial number of radioactive atoms at time t = 0
- λ is the decay constant, which represents the rate of decay for the radioactive isotope
- t is the time elapsed since t = 0
- e is the mathematical constant approximately equal to 2.718
This equation shows that the number of radioactive atoms decreases exponentially over time. The value of the decay constant, λ, determines the rate of decay, and is unique to each radioactive isotope. A higher value of λ means a faster rate of decay, and a lower value of λ means a slower rate of decay.
c) Describe the significance of decay curve showing the longest life time
of radio-isotopes. 1
Answer = The significance of a decay curve showing the longest life time of radioisotopes is that it provides information about the stability of the isotope. A decay curve is a graph that plots the number of radioactive atoms as a function of time. The longest life time of a radioisotope is the amount of time it takes for half of the radioactive atoms to decay. This information is useful in determining the half-life of the radioisotope, which is an important parameter for characterizing its behavior and for predicting its future behavior in various applications.
d)The half-life of radium is 1620 years. After how many years 25% of a
radium block remains undecayed ? 3
Answer = The half-life of a radioactive isotope is defined as the time it takes for half of the initial amount of the isotope to decay. If the half-life of radium is 1620 years, then after half-life period (1620 years), half of the initial amount of radium will remain undecayed and half will have decayed.
To find the time it takes for 25% of a radium block to remain undecayed, we can use the radioactive decay law:
N = N0 * e^(-λt)
Where N is the amount of radium remaining after time t, N0 is the initial amount of radium, λ is the decay constant, and e is the base of the natural logarithm.
Setting N equal to N0 * 0.25, we can solve for t:
N0 * 0.25 = N0 * e^(-λt)
Taking the natural logarithm of both sides:
ln (0.25) = ln (e^(-λt))
Using the properties of logarithms:
ln (0.25) = -λt * ln (e)
Dividing both sides by -λ * ln (e):
t = ln (0.25) / -λ
Since the half-life of radium is 1620 years, we can use that to find the decay constant λ:
λ = ln (2) / half-life = ln (2) / 1620 years
Substituting this value of λ into the equation for t:
t = ln (0.25) / -λ = ln (0.25) / (ln (2) / 1620 years)
Thus, after approximately 3244 years, 25% of a radium block will remain undecayed.
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