Test: Self Inductance - 1

Concept:

• 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

Induced e.m.f can be given as:

Where V_L = induced voltage in volts, L = self-inductance of the coil, dl/dt = rate of change of current in ampere/second.

Calculation:
Given:
I₁ = +2 Amp, I₂ = -2 Amp, dt = 0.05 sec, VL = 8 volt
⇒ dI = I₂ - I₁ = (-2 - 2) = -4 Amp
From equation 1,

Concept:

• The self-inductance of a coil is defined as the ratio of the magnetic flux and the current flowing through it.
• In a conducting coil, magnetic flux is the product of the magnetic field due to the current flowing in the coil and the area of the coil.
• According to Faraday's law, in a conducting wire, the change in electric current changes the magnetic flux associated with it, and the change in the magnetic flux induces an electric current.
• According to Lenz law, the direction of the induced current is such that the initial change in the electric current is opposed.
• As soon as the change in electric current stops, the induced current also stops flowing.
• The formula to calculate the electromotive force due to induction is, 

Where E is the electromotive force or the potential, t is the time elapsed, L is the self-inductance of the coil and ΔI is the change in the electric current of the coil.

• The S.I unit of self-inductance is Henry(H).

Calculation:
Given: E = 5 V, t = 1 ms = 0.001 s, ΔI = (2A - 3A) = - 1A
According to Faraday's Law,

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:

• 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:

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

Explanation:

 μ_o ,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.

Concept:

• 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 –
  

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

Explanation

Given - l₂ = 2l₁

• Self-inductance of a solenoid is given by:
  
• According to the question, the length of the solenoid is doubled without any change in the number of turns and the area of the coil
  

Concept:

• The coil which stores magnetic energy in a magnetic field is called an inductor.
• The property of an inductor which causes the emf to generate by a change in electric current is called as inductance of the inductor.
• The SI unit of inductance is Henry (H).
• The magnetic potential energy stored in an inductor is given by,

Where L is inductance of the inductor and I is current flowing.

Explanation:
Given that:
Magnetic potential energy (U) = 25 mJ = 25 x 10^-3 J
Current (I) = 60 mA = 60 x 10-3A
Use the formula:

Concept:

• 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
  

Explanation:

• Self-inductance of a solenoid is given by 
  
• From the above equation, it is clear that the self-inductance of a solenoid depends on the geometry and magnetic permeability of the core material.  
• It is independent of current, so if we increase the current in an inductor, there will be no change in the self-inductance of the inductor. Therefore the correct answer is option 3.

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 –
  

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 –
  

Dependence of mutual inductance –

• The number of turns (N₁, N₂) of both coils.
• Area of the cross-section of coils.
• The magnetic permeability of medium between the coils (μ_o) or nature of the material on which two coils are wound.
• Length of the coil (l).
• From the above formula, mutual inductance of two coils can be increased by increasing the number of turns in the coils.

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.
  • The self-inductance of a solenoid is given by:
    

Where N = number of turns, A = area of cross-section, l = length of the solenoid and μ₀ = absolute permeability 

Calculation:
Give - L₁ = 0.18 mH = 0.18 x 10^-3 H , μ₁ = μ_₀μ, μ₂ = μ_₀ and relative permeability (μ) = 900 

The self-inductance of a solenoid is given by:

Here N, A and l is constant
∴ L ∝ μ 

Concept:

Self-induction:

• When current flows through a coil or circuit, the magnetic field is produced and hence a magnetic flux gets associated with this coil or circuit.
• This magnetic flux is directly proportional to the current flowing in the circuit.
• If the current through the coil is changed, the magnetic field also changes, and hence the magnetic flux associated with it also changes, and as a result of this, an emf is induced in the coil or circuit.
• This phenomenon is called self-induction.

Lenz's Law:

• According to this law, the emf will be induced in a coil due to a changing magnetic flux in such a way that it will oppose the cause which has produced it.
• This law states that the induced emf in a conductor due to a changing magnetic flux is such that the magnetic field created by the induced emf opposes the change in a magnetic field.
  

  where N = number of loops and dϕ =  Change in magnetic flux

  The above equation is given by Faraday's law, but the negative sign is a result of Lenz's law.

Explanation:

• If the magnitude of the applied potential is decreased in the coil, the current in the coil also decreases, and due to the self-induction, an emf will get induced in the coil due to which a current will also induce in the coil.
• According to Lenz's law, the direction of induced emf is such that it always opposes change due to which it is produced.
• So here the current in the coil is decreasing, so the induced emf will try to increase it, therefore the direction of the induced current will be the same as the ​current due to applied potential.
• Hence, option 2 is correct.