Electromagnetic Induction and Inductance MCQ Quiz - Objective Question with Answer for Electromagnetic Induction and Inductance - Download Free PDF

Calculaton:

Given, I = 2 A and di/dt = +1 A/s

The correct answer is Soft Iron.

Key Points

• Soft iron is defined as iron that can easily be magnetized and demagnetized with a small quantity of hysteresis loss and has a low carbon content.
• It is used because it does not retain its magnetism power when the current is switched off. 
• In other words, we can understand that it does not become Permanently Magnetized.
• Soft Iron has low coercive force or low coercivity and low retentivity.

• The susceptibility of this iron is very high and very less corrosive.

Additional Information

• Rusted Iron:
  • ​Rusted iron is a result of a process called corrosion, specifically the type known as rusting, which affects iron and its alloys, including steel.
  • The rust itself is generally characterized as a flaky, red-brown substance that causes the iron to become brittle and crumble over time.
  • The formation of rust happens via an electrochemical or oxidation-reduction (redox) reaction, where iron reacts with oxygen and water in the environment to produce iron oxides.
  • The general equation of the rusting process is: 4Fe + 3O₂ + 6H₂O→ 4Fe(OH)₃
• Firm Iron:
  • ​"Firm iron" typically refers to iron that is solid, robust, and of high structural integrity.
  • Iron in its pure form or as used in iron alloys, such as steel, is known for its hardness and tensile strength, making it a versatile material in various applications.
  • Firm iron or structurally robust iron plays a critical role in construction, automobile manufacturing, and consumer goods production due to its durability and malleability.
  • With the addition of carbon, iron is made into steel, an incredibly strong and versatile material.
• Hard Iron:
  • ​"Hard iron" typically refers to iron that has been processed or alloyed in a way to make it harder and more durable.
  • Iron, in its pure form, is fairly soft.
  • Therefore, other materials like carbon are commonly added to increase their hardness and tensile strength, creating iron alloys such as steel.
  • The process of making "hard iron" often involves heat treatments like tempering and quenching.
  • This manipulates the consistency and structure of the metal to help improve its hardness, toughness, and overall durability.

\( U=\dfrac {1}{2}Li^2 \ Rate=\dfrac {dU}{dt}=(Li)\left (\dfrac {di}{dt}\right ) \)

\( at\ t=0, i=0, \therefore rate=0 \)

It is only the curve A that has zero initial value and a value at infinity approaching zero.

Explanation:

emf = \( L \dfrac{di}{dt} \) Rate of change of current is constant for one period at a positive value and is constant at a negative value for the second time period.

Therefore emf is a constant positive value for the first half and a constant negative value for the second half.

∴ Option C is correct.

Concept:

The power dissipated in the RC circuit depends on both the resistor and the capacitor.

The impedance for the RC circuit is given by:

Z_RC = [(R₂ + (1/ωC)²)]^1/2

The power factor for an RC circuit is: cos(φRC) = R / Z_RC

​Explanation:

• The power dissipated in the RC circuit is:
  • P1 = (V²_rmsR) / Z²RC
  • The power dissipated in the RL circuit depends on both the resistor and the inductor.
• The impedance for the RL circuit is given by:
  • Z_RL = [(R₂ + (ωL)²)]^1/2
  • The power factor for an RL circuit is:
  • cos(φRL) = R / Z_RL
• The power dissipated in the RL circuit is:
  • P2 = (V²_rms R) / Z²_RL
• In an LC circuit, the inductive reactance and capacitive reactance cancel each other out when
  • ωL = 1/ωC.
• This results in a purely reactive circuit with no real power dissipation. Hence, the power in the LC circuit is:
  • P3 = 0

Thus, Both the RC and RL circuits dissipate real power, and because both involve resistive elements, they will dissipate the same amount of power.
The LC circuit, being purely reactive, dissipates no real power.
P1 = P2 > P3 

∴ The correct option is 3

The correct answer is magnetic flux.

 Key Points

• Magnetic flux is a measurement of the total magnetic field which passes through a given area.
• Magnetic flux is the product of the average magnetic field times the perpendicular area that it penetrates.
• The SI unit of magnetic flux is Weber (Wb).

 Important Points

• Conductance explains the ease with which electric current flows through a substance.
• Magnetic flux density is defined as the amount of magnetic flux in an area taken perpendicular to the magnetic flux's direction.
• Capacitance is the ability of a body to hold an electrical charge.

CONCEPT:

• Potential energy: Potential energy is the energy stored within an object, due to the object's position, arrangement or state.
• Heat energy: Heat is the transfer of energy from one system to another, and it can affect the temperature of a singular system.
• Kinetic energy: Kinetic energy is the energy of mass in motion. The kinetic energy of an object is the energy it has because of its motion.
• Radiation energy: Radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium.

EXPLANATION:

• The work done by moving coil (Change in kinetic energy) induces the electrical energy in the conductor.

This principle is used in electric generators.

So option 3 is correct.

CONCEPT:

• Magnetic flux: The number of magnetic field lines passing through a surface area normally is called magnetic flux. It is denoted by ϕ.
• Magnetic flux is mathematically equal to the dot product of the magnetic field and area vector through which it is passing.

\(⇒ {ϕ}=\vec{B}\cdot\vec{A}=BAcos\,θ\)

Where B = magnetic field, A = area vector, and θ = angle between B and A

• The SI unit of magnetic flux is weber (Wb).
• Electric field: The space or region around the electric charge in which electrostatic force can be experienced by other charged particles is called an electric field by that electric charge.
• Electric flux (ΦE): The electric flux through a given area held inside an electric field is the measure of the total number of electric lines of force passing normally through that area.

EXPLANATION:

• The number of magnetic field lines passing through a surface area normally is called magnetic flux. So option 2 is correct.

CONCEPT:

• An electromagnet is a temporary magnet which should ideally have the property to behave as a magnet when current passes through it and lose magnetism as soon as current is stopped.
• Soft iron is generally used for making electromagnets because it has high magnetic permeability, i.e. it can easily gain magnetic properties when current is passed around the core and quickly lose when current is stopped.
• The soft iron inside the coil makes the magnetic field stronger because it becomes a magnet itself when the current is flowing

EXPLANATION:

• As the electromagnet is a temporary magnet is only works till when we give the current to it.
• Once the electric current is stopped the magnetic property of the electromagnet vanished.

CONCEPT:

Mutual Induction: 

• Whenever the current passing through a coil or circuit changes, the magnetic flux linked with a neighboring coil or circuit will also change.
• Hence an emf will be induced in the neighboring coil or circuit. This phenomenon is called ‘mutual induction’.
  • Mutual induction between the two coils of area A, number of turns N1 and N2 with the length of secondary or primary l is given by:

\(⇒ M = - \frac{{{e_2}}}{{\frac{{d{I_1}}}{{dt}}}} = - \frac{{{e_1}}}{{\frac{{d{I_2}}}{{dt}}}}\)

EXPLANATION:

• Mutual induction between the two coils of area A, number of turns N1 and N2 with the length of secondary or primary l is given by:

\(⇒ M = - \frac{{{e_2}}}{{\frac{{d{I_1}}}{{dt}}}} = - \frac{{{e_1}}}{{\frac{{d{I_2}}}{{dt}}}}\)

• As we know, the dimension of the electric potential is

⇒ e = [ML²T^-3A^-1]

• The dimension of dI/dt is

\(⇒ \frac{dI}{dt} = [AT^{-1}]\)

• Therefore, the dimension of mutual Induction is

\(⇒ M = \frac{[ML^2T^{-3}A^{-1}]}{[AT^{-1}]}= [ML^2T^{-2}A^{-2}]\)

Additional InformationSelf-Induction:

Whenever the electric current passing through a coil changes, the magnetic flux linked with it will also change.

• As a result of this, in accordance with Faraday’s laws of electromagnetic induction, an emf is induced in the coil which opposes the change that causes it.
• This phenomenon is called ‘self-induction’ and the emf induced is called back emf, current so produced in the coil is called induced current.
  • The self-inductance of a solenoid is given by:

\(⇒ L = \frac{{{\mu _o}{N^2}A}}{l}\)

CONCEPT:

• AC Generators: A machine that converts mechanical energy into electrical energy is AC generators.
  • This electrical energy is in the form of an alternating current of the sinusoidal output waveform.
  • This mechanical energy is generally supplied by gas turbines, steam turbines, and combustion engines. 
• AC generators work on the principle of Faraday’s law which explains electromagnetic induction.
  • This can either be achieved by rotating the magnetic field that contains the stationary conductor or by rotating a conducting coil in a static magnetic field.
  • So it is preferred to keep the coil stationary because it is easier to draw induced alternating current from a stationary armature coil than a rotating coil.

EXPLANATION:

• The device in which electrical energy is converted into mechanical energy is called an electric motor.
• AC generator works on the principle of Faraday's Law.
  • AC generators convert mechanical energy into electrical energy.
  • The generated energy is in the form of a sinusoidal waveform (alternating current). Therefore option 2 is correct.
• An ammeter is an instrument that is used to measure the current flowing through the circuit.
  • It has low resistance, ideally zero.
  • By connecting ammeter in series, it allows all of the circuit current to pass through it and hence measure it.
• Galvanometer: An electro-mechanical instrument used for indicating and detecting electric current.
  • A galvanometer works as an actuator.
  • It produces a rotary deflection, in response to electric current flowing through the coil in a constant magnetic field.

Faraday’s first law of electromagnetic induction states that whenever a conductor is placed in a varying magnetic field, emf is induced which is called induced emf. If the conductor circuit is closed, the current will also circulate through the circuit and this current is called induced current.

Faraday's second law of electromagnetic induction states that the magnitude of emf induced in the coil is equal to the rate of change of flux that linkages with the coil. The flux linkage of the coil is the product of number of turns in the coil and flux associated with the coil.

CONCEPT:

• Eddy Current: When a changing magnetic flux is applied to a bulk piece of conducting material then circulating currents is called eddy currents are induced in the material.
  • Because the resistance of the bulk conductor is usually low, eddy currents often have large magnitudes and heat the conductor.

EXPLANATION:

• Eddy currents are the currents induced in solid metallic masses when magnetic flux threading through them changes.
• Eddy current is also known as“Focault current”.
• Eddy current also opposes the change in magnetic flux, so there is given by Lenz’s law. 

CONCEPT:

• Magnetic flux is total magnetic field that passes through the given area.
• If we choose a simple flat surface with area A and there is an angle θ between the normal to the surface and a magnetic field vector (magnitude B) then the magnetic flux is ϕ = BA cosθ 

• Faraday's Law: Any change in the magnetic flux of wire will cause a voltage (induced emf) to be "induced" in the coil.
• This change can be produced by changing the magnetic field strength, moving the coil into or out of the magnetic field,  moving a magnet toward or away from the coil,rotating the coil relative to the magnet, etc.
• Induced emf \(=-N \frac{\Delta \phi }{\Delta t}\)

CALCULATION:

Given that N=50 turns

​\( \frac{\Delta \phi }{\Delta t}\)= 0.05 Wb/s

induced emf  \(=-N \frac{\Delta \phi }{\Delta t}\)

= 50 × 0.05 = 2.5 Volt

So, The correct answer is Option 1, i.e 2.5 V

• Lenz's law says that the direction of the induced current in coil will be always in such a way as to oppose the change which produces the current.
• It is just a small addition to Faraday's law. See negative sign in the formula. Negative sign shows opposement.

CONCEPT:

• Self-Induction: Whenever the electric current passing through a coil changes, the magnetic flux linked with it will also change.
  • As a result of this, in accordance with Faraday’s laws of electromagnetic induction, an emf is induced in the coil which opposes the change that causes it.
  • This phenomenon is called ‘self-induction’ and the emf induced is called back emf, current so produced in the coil is called induced current.

Self-inductance of a solenoid is given by:

\(L=\frac{{{\mu }_{o}}{{N}^{2}}A}{l}\) -- (1)

Where μo = Absolute permeability, N = Number of turns, l = length of the solenoid, and A = Area of the solenoid.

EXPLANATION:

 μo ,I, A are constants. So, we can say that 

L = k N² -- (2)

k is constant, N is the number of turns

L is directly proportional to the square of a number of turns.

If number of turns becomes N' = N², then inductance 

L' = k N' ² 

⇒ L' = k (2N)² = k 4 N² = 4 K N²

⇒ L' = 4 L

So, the inductance is increased by 4 times.

Hence the correct option is 4 times.

Important Points

Induced e.m.f can be given as

\(⇒ e =- L\frac{{di}}{{dt}}\)