Physics: CUET Mock Test - 10 - CUET MCQ

A P-type semiconductor is formed when a trivalent electron deficient impurities such as boron group elements are doped with intrinsic semiconductor. As the impurities are electron deficient, they take electrons from the valence band creating a number of holes. Due this reason conductivity in P-type semiconductor is mainly due to holes rather than electrons.

The magnitude of the induced emf can be calculated using Faraday's law of electromagnetic induction, which states that the magnitude of the induced emf is equal to the rate of change of magnetic flux through the loop.

The magnetic flux through the loop is given by:
Φ = BAcosθ
where B is the magnetic field strength, A is the area of the loop, and θ is the angle between the magnetic field and the normal to the loop.

In this case, the loop is a rectangle with one side being the length of the rod and the other side being the width of the loop, which is not given. However, we can assume that the width is much smaller than the length, so we can approximate the area of the loop as A = L*w, where L is the length of the rod and w is the width of the loop. Thus, we have:
Φ = BLw*cosθ

The angle θ is 0 degrees because the magnetic field is perpendicular to the plane of the loop, so we have:
Φ = BLw

The rate of change of magnetic flux is given by:
dΦ/dt = BL(dw/dt)
where dw/dt is the rate at which the width of the loop is changing, which is equal to the speed of the rod,

Therefore, the induced emf is given by:
emf = -dΦ/dt = -BL(dw/dt)
emf = -BVL

Calculation:

From the above-derived formula, the induced emf is given as
E = BVL

Given that
v = 12 cm/s.= 0.12 m/s
B = 0.50 T
L = 15 cm = 0.15 cm
E = -0.5 × 0.12 × 0.15 = -9 × 10^-3 V.

The negative sign indicates that the direction of the induced emf is opposite to the direction of the motion of the rod
The magnitude of emf = 9 × 10-3 V.

The correct answer is option (2)

Force (F) when K is closed is given by a formula B × L × I.
B = 0.5 T
L = 0.15 m
Since we have calculated induced emf V = 9 × 10^-3 Volts
Induced current = V/R
= 9 × 10^-3/0.18
= 50 × 10^-3 A.
F = BIL
= 0.5 × 50 × 10^-3 × 0.15
= 3.75 × 10-3 N.
The correct answer is option (4)

Power dissipation is given by the formula E²/R
Induced emf is given as
E = BVL

Given that:
B = 0.5 T
V = 12 cm/s = 0.12 m/s
L = 15 cm = 0.15 m.
R = 180 mΩ = 0.18 Ω

Calculating E
E = 0.5 × 0.12 × 0.15
= 9 × 10^-3 Volts
Power P = E2/R
= (9 × 10-3)²/0.18
= 4.5 × 10-4 W
The correct answer is option (3)

Calculation:
Given that:
Velocity = 12 cm/sec = 0.12 m/sec
Length of Rod = 15 cm = 0.15 m
B = 0.5 T.
Resistance R = 180 mΩ = 0.18 Ω
To calculate the power dissipated as heat, we need to first calculate the current flowing.
Since the induced emf is calculated as
E = BVL
= 0.5 × 0.12 × 0.15
= 9 × 10^-3 Volts.
The current I would be equal to
I = E/R
I = 9 × 10-3/(0.18)
= 50 × 10^-3 A
The power dissipation is equal to
P = I²R
= (50 × 10-3 )² × 0.18
P = 4.5 × 10^-4 Watt
The correct answer is option (4)

The correct answer is option "4"

Concept:
According to Faraday's law of electromagnetic induction, a changing magnetic field induces an electric field and thus an EMF in a conductor.

The induced EMF (ε) in a conductor is given by the formula:
ε = - dΦ/dt
where dΦ/dt is the rate of change of magnetic flux through a surface bounded by the conductor. The negative sign indicates that the induced EMF is always in a direction to oppose the change in magnetic flux that produced it, according to Lenz's law.

The magnetic flux (Φ) through a surface is given by the formula:
Φ = B * A * cos(theta)
where
B is the magnetic field strength,
A is the area of the surface, and
theta is the angle between the magnetic field and the surface normal.

If the surface is a loop of wire with a length L moving at a velocity v perpendicular to the magnetic field B, then the area of the loop swept out by the motion is A = L * v, and the angle between the magnetic field and the surface normal is theta = 0.

Therefore, the magnetic flux through the loop is given by:
Φ = B * L * v * cos(0) = B * L * v

The rate of change of magnetic flux through the loop is then:
dΦ/dt = B * L * dv/dt = B * L * a
where a is the acceleration of the loop.

Substituting this expression for dΦ/dt into the equation for the induced EMF, we get:
ε = - B * L * a

So, if the magnetic field strength B, the length of the conductor L, and the velocity of the conductor v are given, the induced EMF can be calculated using the above formula, provided that the acceleration of the conductor is also known.

Note that this formula only applies when the conductor is moving perpendicular to the magnetic field. If the conductor is moving at an angle to the magnetic field, then the formula for the magnetic flux through the surface must take into account the component of the area perpendicular to the magnetic field, and the angle between the magnetic field and the surface normal.

Calculation:

The induced EMF produced in a moving rod is given by the formula:

EMF = B L v sin(theta)
where B is the magnetic field strength, L is the length of the rod, v is the velocity of the rod, and theta is the angle between the direction of motion of the rod and the magnetic field.

• If the magnetic field becomes parallel to the rails, then the angle between the direction of motion of the rod and the magnetic field is zero, i.e. theta = 0. In this case, the sine of theta becomes zero, and therefore the induced EMF becomes zero.
• So, if the magnetic field becomes parallel to the rails instead of being perpendicular, the induced EMF produced in the moving rod will be zero.

Concept:

The electron in the nth orbit is given as,

Bohr radius is symbolized by a

Where, ϵ₀ = 8.854 × 10^-12 Fm is the permittivity in air.

m = 9.109 × 10^-31 kg is the mass of the electron

e = 1.6 × 10^-19 C is the charge of the electron

Z = atomic number

​Explanation:

The electron in the nth orbit is given as,

For Hydrogen as, Z = 1

r_n = a₀ n²

CONCEPT:

Hydrogenic atoms:

• Hydrogenic atoms are atoms consisting of a nucleus with positive charge +Ze and a single electron, where Z is the proton number.
• Examples are a hydrogen atom, singly ionized helium, doubly ionized lithium, and so forth.

De Broglie's Explanation of Bohr's Second Postulate of Quantisation:

• Bohr's second postulate states that the electron revolves around the nucleus only in those orbits for which the angular momentum is some integral multiple of h/2π where h is the Planck’s constant (6.6×10-34 J-sec).
• Thus the angular momentum (L) of the orbiting electron is quantized.
• So the angular momentum of the electron orbiting in the nth orbit around the nucleus is given as,

• Louis de Broglie argued that the electron in its circular orbit, as proposed by Bohr, must be seen as a particle wave.
• For an electron moving in the nth circular orbit of radius rn, the total distance is the circumference of the orbit.
• If the wavelength of the electron orbiting in the nth circular orbit is λ, then,

⇒ 2πrn = nλ

• We know that the De Broglie wavelength of the electron moving with speed vn in the nth orbit is given as,

CALCULATION:

Given v₁ = v and v₂ = 2v

Where v1 = initial speed of the electron and v2 = final speed of the electron

• We know that the De Broglie wavelength of the electron moving with speed vn in the nth orbit is given as,

-----(1)

• When the speed of the electron is v₁, the De Broglie wavelength of the electron is given as,

-----(2)

• When the speed of the electron is v2, the De Broglie wavelength of the electron is given as,

-----(3)

By equation 2 and equation 3,

• Hence, option 2 is correct.

Additional Information

Limitations of the Bohr model:

1. The Bohr model is applicable to hydrogenic atoms. It cannot be extended even to mere two-electron atoms such as helium. The analysis of atoms with more than one electron was attempted on the lines of Bohr’s model for hydrogenic atoms but did not meet with any success. The formulation of the Bohr model involves electrical force between the positively charged nucleus and electron. It does not include the electrical forces between electrons which necessarily appear in multi-electron atoms.
2. Bohr’s model correctly predicts the frequencies of the light emitted by hydrogenic atoms, the model is unable to explain the relative intensities of the frequencies in the spectrum.

Concept:

The kinetic energy is defined as the energy stored in an object because of its motion.

When subatomic particles (electron, proton, etc.) behave like a wave then the wavelength is called de Broglie wavelength

• 
• p = mv
• λ = de Broglie wavelength, h = Planck constant, p = momentum of the subatomic particles, m = mass of subatomic particles, v = velocity of subatomic particles
• Mass of electron = 9.1093837015 × 10⁻³¹ kg
• Speed of light, c = 3 × 10⁸ m/s

Kinetic energy of photon,

• Speed of light, c = 3 × 10⁸ m/s

Calculation:

Given, de-Broglie wavelength, λ = 10^-10 m

Let the kinetic energy of electron is E,

Also,

---- (1)

For the case of a photon,

---- (2)

Dividing equation (2) by (1), we get

Substituting value,

Clearly, E' is greater than E, so the photon has greater kinetic energy than electron

A diode can have two different capacitances:

Diffusion Capacitance:

It is dominant when the diode is forward and is the result of storage charges when forward biased.

The diffusion capacitance is given by the formula:

---(1)

IDQ = Quiescent current of the diode.

τ = Minority carrier lifetime

VT = Thermal voltage

Since the diode current Equation is given as:

---(2)

From Equation (1) and (2), we conclude that the diffusion capacitance increases exponentially with forward bias voltage (Vf).

Junction Capacitance:

It is dominant when the diode is reverse biased and is the result of the charge stored in the Depletion layer.

The junction capacitance is given by the formula:

W = depletion region width

• A p-n junction is formed when a p-type and an n-type semiconductor is joined together.
• It is the basic building block of many devices.
• At the junction the electrons diffuse from n side to p side because of the process of diffusion which states that an entity will flow from an area of higher concentration to that of a lower one.
• Since electrons are the majority charge carriers on the n-side, therefore electrons move from high density area of n-side to low density area of p-side.

The materials can be classified by the energy gap between their valence band and the conduction band. The valence band is the band consisting of the valence electron, and the conduction band remains empty. Conduction takes place when an electron jumps from valence band to conduction band and the gap between these two bands is forbidden energy gap. Wider the gap between the valence and conduction bands, higher the energy it requires for shifting an electron from valence band to the conduction band.In the case of conductors, this energy gap is absent or in other words conduction band, and valence band overlaps each other. Thus, electron requires minimum energy to jump from valence band. The typical examples of conductors are Silver, Copper, and Aluminium.In insulators, this gap is vast. Therefore, it requires a significant amount of energy to shift an electron from valence to conduction band. Thus, insulators are poor conductors of electricity. Mica and Ceramic are the well-known examples of insulation material. Semiconductors, on the other hand, have an energy gap which is in between that of conductors and insulators. This gap is typically more or less 1 eV, and thus, one electron requires energy more than conductors but less than insulators for shifting valence band to conduction band.

In P-type doping, boron or gallium is the dopant. Boron and gallium each have only three outer electrons. When mixed into the silicon lattice, they form "holes" in the lattice where a silicon electron has nothing to bond to. The absence of an electron creates the effect of a positive charge, hence the name P-type.Holes can conduct current. A hole happily accepts an electron from a neighbor, moving the hole over a space. P-type silicon is a good conductor.

Materials that have the resistance levels between those of a conductor and an insulator are referred to as semiconductors.They are quite common, found in almost all electronic devices. Good examples of semiconductor materials are germanium, selenium, and silicon.Radium is a chemical element with symbol Ra and atomic number 88. It is the sixth element in group 2 of the periodic table, also known as the alkaline earth metals.

An intrinsic semiconductor, also called an undoped semiconductor or i-type semiconductor, is a pure semiconductor without any significant dopant species present. The number of charge carriers is therefore determined by the properties of the material itself instead of the amount of impurities. In intrinsic semiconductors the number of excited electrons and the number of holes are equal: n = p.

Doping is the process of adding impurities to intrinsic semiconductors to alter their properties. Normally Trivalent and Pentavalent elements are used to dope Silicon and Germanium. When an intrinsic semiconductor is doped with Trivalent impurity it becomes a P-Type semiconductor.

The electron theory states that all matter is composed of atoms and the atoms are composed of smaller particles called protons, electrons, and neutrons. The electrons orbit the nucleus which contains the protons and neutrons. It is the valence electrons that we are most concerned with in electricity. These are the electrons which are easiest to break loose from their parent atom. Normally, conductors have three or less valence electrons; insulators have five or more valence electrons; and semiconductors usually have four valence electrons.

A pure semiconductor is called intrinsic semiconductor, e.g., silicon, germanium. The presence of the mobile charge carriers is the intrinsic property of the material. At room temperature, some covalent bonds are broken and electrons are made free. The absence of electron in the covalent bond form hole.The electrical conduction is by means of mobile electrons and holes. Hole act as positive charge, because it can attract an electron. If some other bond is broken and the electron thus freed fills this hole(vacancy), it seems as though the hole is moving.Actually an electron is travelling in opposite direction. In a pure(intrinsic) semiconductor, the number of holes is equal to the number of free electrons.

Most vibrating objects have more than one resonant frequency and those used in musical instruments typically vibrate at harmonics of the fundamental. A harmonic is defined as an integer (whole number) multiple of the fundamental frequency.

In communication the Transmitter helps in transmitting the signal through communication channel which acts as a physical path that connects transmitter to a receiver.And the receiver receives the transmitted signal and converts those signals in their original form.

As the information or message is transmitted from the source to the receiver ,it is first converted into electrical signal which is then transmiited through the communication medium.Hence in electrical communication it is must to convert raw message or information into electrical signal.Else the electronic messages will not be transmitted.

In point to point communication,communication occurs over a link between a single transmitter and receiver.Telephony is an example of it as it needs a link between caller and receiver to transmit the information.This link is provided by various media like cable.

In broadcast mode of communication a large number of receivers are linked to a single transmiiter.Radio works as receiver which converts the transmiited information/message into the original form of the information.

The earth's magnetic field is Be​ and its horizontal and vertical components are H_e​ and H_v​
cosθ= H_e​​/B_e​
∴cos60^o= (​0.26×10^−4​/ B_e )T
⇒B_e​=(​0.26×10⁻⁴)/ (½)​=0.52×10⁻⁴T=0.52G

Magnetic poles exist in pairs. It is not possible to isolate a north pole or a south pole. Magnetic field lines start from the north pole and go to the south pole and return to the north pole. They form continuous closed loops unlike electric lines of force which do not as an electric monopole, a single charge does exist.

For paramagnetic materials orbital and spin magnetic moments of the electrons are of the order of bohr magneton.
Paramagnetic materials have some unpaired electrons due to these unpaired electrons the net magnetic moment of all electrons in an atom is not added up to zero. Hence atomic dipole exists in this case. On applying external magnetic field the atomic dipole aligns in the direction of the applied external magnetic field. In this way, paramagnetic materials are feebly magnetized in the direction of the magnetizing field.

Spin and Orbital angular momentum arise due to the presence of unpaired electrons. If there are unpaired electrons, these momenta will be there otherwise not.

The magnitude of induced emf is independent of the resistance of the coil.
∴ e = −dϕ/dt = −N (d/dt) [(BA)/dt]
Thus, e depends upon N, B and A.
But induced current depends upon R.

In an iron cored coil the iron core is removed so that the coil becomes an air cored coil. The inductance of the coil will decrease.

Induced emf = Blv = 12V. It is induced in the northward direction by right hand rule (emf=)
therefore if the south end of the pole has potential of 0V, the north end will have a potential of 12V.