Semiconductor

Step 1: Understanding the Concept:
The thermal voltage ( ) is a parameter that appears in the equations governing semiconductors. It represents the average thermal energy per unit charge and is directly proportional to the absolute temperature.
Step 2: Key Formula or Approach:
The formula for thermal voltage is:
where:
= Boltzmann's constant ( J/K)
= Absolute temperature in Kelvin (K)
= Elementary charge ( C)
Step 3: Detailed Explanation:
1. Convert Temperature to Kelvin:
The given temperature is 47°C. To convert to Kelvin, we add 273.15 (or often just 273 for simplicity).
2. Substitute the values into the formula:
3. Convert to millivolts (mV):
To convert from Volts to millivolts, we multiply by 1000.
Step 4: Final Answer:
The calculated value is approximately 27.6 mV, which matches option (A).

Concept: For a body rolling without slipping down an incline, acceleration depends on both translational and rotational motion.
Step 1: General formula.
For rolling motion:
Step 2: Moment of inertia of solid sphere.

Step 3: Substitute in formula.

Step 4: For .

Step 5: Evaluating the options.

• Incorrect
• Missing (incorrect)
• Correct
• Incorrect

Step 6: Conclusion.
Thus, acceleration is .

Concept: The quality factor ( ) of a resonant circuit measures the sharpness of resonance.
Step 1: Definition of quality factor.
It is defined as the ratio of resonant frequency to the bandwidth of the circuit.
Step 2: Formula.
where is the resonant frequency and is the bandwidth.
Step 3: Physical meaning.
Higher means sharper resonance and lower energy loss.
Step 4: Evaluating the options.

• Incorrect
• Correct
• Incorrect
• Incorrect

Step 5: Conclusion.
Thus, .

Concept: Forward biasing of a P-N junction diode reduces the barrier potential and allows current to flow.
Step 1: Understanding diode structure.
A P-N junction consists of a P-type semiconductor (holes as majority carriers) and an N-type semiconductor (electrons as majority carriers).
Step 2: Forward bias condition.
In forward bias, the external voltage is applied such that it reduces the depletion region.
Step 3: Connection of terminals.
The P-side is connected to the positive terminal, and the N-side is connected to the negative terminal.
Step 4: Evaluating the options.

• Negative terminal Connected to N-side (incorrect)
• Positive terminal Connected to P-side (correct)
• Ground Not specific (incorrect)
• Neutral terminal Not applicable (incorrect)

Step 5: Conclusion.
Thus, the P-side is connected to the positive terminal during forward biasing.

Concept: The motion of satellites follows Kepler’s third law of planetary motion.
Step 1: Kepler’s third law.

Step 2: Deriving the relation.
Taking square root on both sides:
Step 3: Understanding the result.
As the distance from Earth increases, the orbital period increases more than linearly.
Step 4: Evaluating the options.

• Incorrect
• Incorrect
• Correct
• Incorrect

Step 5: Conclusion.
Thus, .

Concept: Brewster’s Law states that at a particular angle of incidence (polarizing angle), the reflected light is completely plane polarized.
Step 1: Brewster’s Law formula.
where is the refractive index and is the polarizing angle.
Step 2: Physical meaning.
At this angle, the reflected and refracted rays are perpendicular to each other.
Step 3: Evaluating the options.

• Incorrect
• Incorrect
• Correct
• Incorrect

Step 4: Conclusion.
Thus, the relation is .