Electromagnetic Induction

In a solar cell, when light (photons) falls on the semiconductor material, it generates electron-hole pairs by exciting electrons in the material. These electron-hole pairs are then separated by the electric field present in the solar cell. The separation allows the electrons to move through the material, generating an electric current. Finally, the electrons and holes are collected at the respective electrodes, which generates the emf. Therefore, the process involves the generation, separation, and collection of electron-hole pairs.
Thus, the correct answer is that emf generation in a solar cell happens due to the generation, separation, and collection of electron-hole pairs.

The correct option is (D) : generation, separation and collection of electron-hole pairs

A transformer operates based on the principle of electromagnetic induction and is designed to work with alternating current (AC). It cannot work with direct current (DC) because a DC supply does not produce the varying magnetic flux needed for the operation of the transformer.
Therefore, the correct mismatch pair is Transformer : D.C. voltage, as a transformer is not used for DC voltage.

The correct option is (D) : Transformer : D.C. voltage

The energy stored per unit volume in a magnetic field (in a solenoid) is given by: where is the magnetic induction and is the permeability of the medium (for vacuum, ). The energy stored per unit volume in an electric field (in a capacitor) is given by: where is the electric field strength and is the permittivity of the medium (for vacuum, ). The ratio of energy stored in the magnetic field to the electric field is: In the case of free space, and , and the speed of light is related to and by: Thus, the ratio becomes:

The correct option is (B) :

The magnetic field at the center of a circular loop carrying a current is given by the formula: where:
is the magnetic field at the center,
is the permeability of free space ( ),
is the current,
is the radius of the loop. We are given:
,
.

Now, we solve for : Simplifying: Solving for : Thus, the current to be sent through the loop is , which is option (D).

In a moving coil galvanometer, the current sensitivity is directly proportional to the number of turns of the coil. The voltage sensitivity is proportional to the number of turns squared. Therefore, when the number of turns of the coil is doubled, the current sensitivity becomes double, while the voltage sensitivity remains unchanged. Hence, the correct answer is that the current sensitivity is doubled, but voltage sensitivity remains unchanged.

The correct option is (D) : the current sensitivity is doubled but voltage sensitivity remains unchanged

Given:

• Length of rod (PQ),
• Amplitude of SHM,
• Frequency of SHM,
• Magnetic field, (perpendicular to plane)

Step 1: Determine Maximum Velocity ( )

For simple harmonic motion, the maximum velocity is given by:

where angular frequency .

Substitute values:

Step 2: Calculate Peak Induced EMF ( )

The induced EMF in a moving rod is:

At peak velocity, the peak EMF is:

Substitute known values:

Conclusion:

The peak induced electro-magnetic force is .

Answer:

Given:

• Internal resistance,
• Magnetic field energy stored,
• Power dissipated as heat,

Step 1: Find the Current ( )

The power dissipated in the resistor is given by:

Solving for :

Step 2: Relate Energy to Inductance ( )

The energy stored in the inductor's magnetic field is:

Solving for :

Given parameters:

• Inductance:
• Current change:
• Time interval:

Induced EMF calculation: (Magnitude: 3.0 V)

Thus, the correct option is (C): 3.0 V.