JEE Main Part Test - 5 - JEE MCQ

Given: N = 2N₁ and B = 2B₁
The magnetic flux through the electric generator when the magnetic field is B, current flowing is A and the number of turns is N
φ = N B A cos θ ....(1)
The magnetic flux through the electric generator when the magnetic field and number of turns of the coil of an electric generator is doubled
φ₁ = N₁ B₁ A cosθ   ...(2)
⇒ φ₁ = (2N)(2B) A cos θ = 4 N B A cos θ = 4φ [∵φ = NBA cos θ]

Force on EF,
F_mag​​=i∫(dl×B)=iLBsin(90−θ)=iLBcosθ
F_mag​​ up the inclined plane.
Component of weight of EF down the inclined plane: mgsinθ
For EF to be in equilibrium, iLBcosθ=mgsinθ
∴iLB=mgtanθ
For F_mag​ to be up the inclined plane, it needs to flow from E to F.

The average power consumed/cycle in an ideal capacitor is 0.
The average power consumed in an ideal capacitor is given as based on the instantaneous power which is supplied to the capacitor:
p_c = iv= (i_m cos ωt)(v_m sin ωt)
p_c = i_mv_m (cos ωt sin ωt)
pc=(i_mv_m/2)sin2ωt
We know that sin ωt = 0
Therefore, average power = 0

Laws of reflection are valid for any surface plane or spherical. Hence the reason is false.

Hence, if the objective lens and the eyepiece lens of a microscope are interchanged that will not meet the criterion of the telescope.

So, the reason is true. But the assertion is false.

AC generator works on the principle of Faraday's Law. The AC Generator's input supply is mechanical energy supplied by steam turbines, gas turbines and combustion engines. The output is alternating electrical power in the form of alternating voltage and current.

AC generators convert mechanical energy into electrical energy. The generated energy is in the form of a sinusoidal waveform (alternating current).

So, all the statements regarding AC generators correct.

The AC circuit containing a resistor, inductor, and a capacitor is called an LCR circuit.

The meanings of inductor, capacitor and resistance are as follows:

• The device which stores magnetic energy in a magnetic field is called an inductor.
• The device that stores electrostatic energy in an electric field is called a capacitor.
• The properties of a conductor which opposes the flow of current are called resistance.

The capacitor and inductor are the storage devices that store the energy in it.

The inductor and capacitor can’t dissipate energy. As the resistance opposes the flow of electric current. So, the resistance of any circuit dissipates the power.

In the given figure, when the metallic plate A is allowed to swing like a simple pendulum between the magnetic poles, the magnetic flux associated with the plate keeps on changing as the plate moves in and out of the region between magnetic poles.

Due to this changing magnetic flux, the eddy currents induced in the plate oppose the motion of the plate. If a slot is cut in plate A area then the area available to the flow of eddy currents is less.

Thus, the pendulum plate with holes or slots reduces electromagnetic damping, and the plate swings more freely.

Therefore, the times taken to by the plate to come to rest will increase when a slot is cut in the plate.

• Strong electromagnets are situated above the rails in some electrically powered trains.
• When the electromagnets are activated, the eddy currents induced in the rails oppose the motion of the train.
• When a changing magnetic flux is applied to a bulk piece of conducting material then circulating currents called eddy currents are induced in the material.
• So, by the above explanation, we can understand that the generation of eddy current depends on the magnetic field but it is independent of the direction of the magnetic field.
• Therefore, the eddy current will also generate when the north and the south poles are replaced with each other and that eddy currents induced in the rails oppose the motion of the train. So, the velocity of the train will decrease.

Given: Self-inductance of first coil (L₁) = 108 mH, Radius of both coils are same i.e., r₁ = r₂ = r, Number of turns of the first coil (N₁) = 200, and Number of turns of the second coil (N₂) = 500
The Self-induction for the first coil is:

The Self-induction for the second coil is:

On dividing equation (1) and (2), we get:

Given:
Voltage across the Resistor R (V_R) = 80 V
Voltage across the Inductor L (V_L) = 40 V
Voltage across the Capacitor C (V_C) = 100 V
For a series LCR circuit, the total potential difference of the circuit is given by:

Putting all the above values in the equation,

According to the second experiment of Faraday and Henry, we can say that when a current-carrying coil is moved towards or away from another coil then an emf gets induced in the coil.

If the circuit is closed in which the coil is connected then a current will also get induced in the coil. The relative motion between the two coils is required to induce a current in the coil.

In the given case when the primary coil is rotated about its axis there will be no relative motion between the primary and the secondary coil.

Since, there is no relative motion between the primary and the secondary coil so no current will induce in the primary coil.

• The Lenz law states that the induced emf in a coil due to a changing magnetic flux is such that the magnetic field created by the induced emf opposes the change in a magnetic field.
• When the north pole of a magnet is moved towards a coil that is connected to a circuit, the distance between the magnet and the coil will reduce, and magnetic flux associated with the coil is increased.
• Due to this change in magnetic flux, an emf will induce in the coil and the direction of the induced emf will be such that it tries to stop the change of magnetic flux.
• Therefore, the direction of current will be such that it stops the motion of the magnet and it is only possible when the north pole is formed on the magnet side of the coil so that the coil can repel the magnet.
• We know that if the current in the coil is clockwise, the face of the coil towards the observer behaves as the south pole and if the current in the coil is anti-clockwise, the face of the coil towards the observer behaves as the north pole.
• So, for the formation of the north pole on the magnet side, the current in the coil will be anti-clockwise when the coil is seen from the magnet side.

We know that if there are two solenoids of equal length and one solenoid is placed coaxially inside the other solenoid then the mutual inductance of solenoid 1 with respect to solenoid 2 will be equal to the mutual inductance of solenoid 2 with respect to solenoid 1.
The mutual inductance of both the solenoids is given as,

Where, n₁ = number of turns per unit length of solenoid 1, n₂ = number of turns per unit length of solenoid 2, r₁ = radius of the inner solenoid, and l = length of both the solenoids
By equation (1) it is clear that the mutual inductance of both the solenoids does not depend on the current in the solenoids.
Therefore, when the current in both the solenoids is doubled, the mutual inductance of both the solenoids S₁ and S₂ will remain unchanged. 

Given: DC voltage EP = 120 V (Primary coil)

• The transformer works on the principle of mutual inductance.
• To induce emf in the secondary coil of the transformer, the magnetic flux associated with the secondary coil must change with respect to time.
• When the DC voltage is applied at the primary coil of the transformer, the magnetic flux associated with the coil will remain constant with respect to time. So the emf will not induce at the secondary coil.
• Therefore, when the DC voltage is applied at the primary coil, the induced emf in the secondary coil will be zero.

• When the magnet oscillates in and out of the spring, it induces an EMF, the direction in which EMF is getting induced will be different.
• Due to the induced EMF, a current will be set up in the coil which will deflect the pointer in the galvanometer in the opposite directions, as the magnet oscillates in and out of the spring an eddy current is set up in it decreases the amplitude of oscillation.
• In short, the EMF will be induced in opposite directions, i.e., Left and Right, as the magnet oscillates in and out of the spring also the eddy current will reduce the amplitude of oscillation as the time goes on (Damping).

• Radiowaves electromagnetic waves have the longest wavelength.
• An electromagnetic wave is a wave radiated by an accelerated or oscillatory charge in which a varying magnetic field is the source of electric field and varying electric field is the source of magnetic field. In simple words we can say that the electromagnetic waves are composed of oscillating magnetic fields and electric fields. The abbreviation for electromagnetic waves is EM waves.
• Charged particles—such as electrons and protons—create electromagnetic fields when they move, and these fields transport the type of energy we call electromagnetic radiation, or light.
• There are basically seven types of electromagnetic waves which are a part of the electromagnetic spectrum. These are radio waves, microwaves, infrared waves, X-rays, gamma rays, ultraviolet waves and visible rays.
• In all these seven electromagnetic waves, radio waves have the longest wavelength and the shortest frequency whereas gamma rays have the shortest wavelength and the shortest frequency.
• So, the final answer is that the radio waves have the longest wavelength among all the electromagnetic waves.

Maxwell’s displacement current is a response to inconsistency in the Ampere’s law.

Maxwell showed that Ampere's circuital law is logically inconsistent. He considered a parallel plate capacitor being charged be a battery. He showed inconsistency of the law in the regions outside the plates of capacitor and just between the plates. To resolve this inconsistency displacement current was introduced by Maxwell.

To find the energy stored in the magnetic field after the current has built up to its equilibrium value, we first need to find the steady-state current in the coil.

When the current reaches its equilibrium value, the coil behaves like a resistor because the back-emf induced by the changing magnetic field is zero. Ohm's law can be applied:

I = V/R

where
I is the current
V is the voltage across the coil (10 V)
R is the resistance of the coil (4 Ω)

Plugging in the values:

Now that we have the steady-state current, we can find the energy stored in the magnetic field using the formula:

where
W is the energy stored in the magnetic field
L is the inductance of the coil (2 H)
I is the steady-state current (2.5 A)

Plugging in the values:

To express this in terms of 10⁻² J, divide by 10⁻²:
6.25 ÷ 10⁻² = 625 
Therefore, the energy stored in the magnetic field after the current has built up to its equilibrium value is 625 × 10⁻² J.

Given t = 10 × 10^-6 m
μ = 1.2
λ = 500 × 10^-9 m
When the glass slab inserted infront of one slit then the shift of central fringe is obtained by

The problem involves a conducting circular loop placed in a uniform magnetic field with its plane perpendicular to the field.

The radius of the loop is expanding at a constant rate, and we are asked to find the magnitude of the induced emf in the loop at an instant when the radius of the loop is 2 cm.

The magnetic flux through a circular loop of radius r and area A = πr² placed in a uniform magnetic field B perpendicular to the plane of the loop is given by:

The induced emf in the loop is given by Faraday's law of electromagnetic induction:

In this case, the radius of the loop is expanding at a constant rate of 10⁻³ m / s , which means that the rate of change of the area of the loop is:

The magnetic flux through the loop is changing at this rate, and the induced emf in the loop is given by:

Therefore, the magnitude of the induced emf in the loop at an instant when the radius of the loop is 2 cm is 50.24 ≃ 50 μV.

The correct answer is option B.

The I.U.P.A.C. name for Fe(C₅H₅)₂ is bis(η⁵ -cyclopentadienyl) iron(II) 
The oxidation state of iron is +2 and is written in parenthesis in roman numerals. Two cyclopentadienyl ligands are coordinated to Fe. The prefix bis indicates 2. η⁵ indicates that the cyclopentadienyl ligands are penta coordinates.

Since both cation & anion constitute coordination sphere so it exhibit coordination isomerism and contains ambident ligand so, it shows linkage isomerism

A complex compound in which the oxidation number of metal is zero is [Ni(CO)_4​]. In this complex, the oxidation number of both metal and ligand is zero.

The oxidation number of metal in the complexes K₄​[Fe(CN)₆​], K₃​[Fe(CN)₆​] and [Pt(NH₃)₄]Cl₂ are +2, +3 and +2 respectively.

O. N. of Al = +3
O. N. of B = + 3
[BF₄]^-
[Al(C₂O₃)₃]^3-

Consider werner’s theroy