Electronic Devices

Given:

• Resistance (R) = 4 Ω
• Inductive reactance (X_L) = 3 Ω

The impedance (Z) of an RL series circuit is calculated by:

Z = √(R² + X_L²)

Substituting the values:

Z = √(4² + 3²) = √(16 + 9) = √25 = 5 Ω

The impedance of the circuit is 5 Ω.

To determine which p-n junctions are forward biased, we analyze the potential connections:

Characteristics of forward bias:

• Positive terminal connected to p-side
• Negative terminal connected to n-side
• Applied voltage overcomes built-in potential

Analysis of each junction:

The forward biased junctions are: (B), (C) and (D) only

Note: Junction (A) is reverse biased as it has opposite connections.

To solve this problem, we need to find the number density of holes in the doped silicon semiconductor. When pentavalent atoms are introduced into silicon, they donate extra electrons to the conduction band, increasing the electron concentration .

First, calculate the number density of donor atoms introduced. Given the pure silicon crystal has atoms/m³ and is doped with 1 pentavalent atom per silicon atoms:

This is the concentration of electrons contributed by the doping. Assuming each donor atom donates one electron, the electron concentration in doped silicon will be approximately equal to .

The intrinsic carrier concentration is given as . In equilibrium, the product of electron and hole concentrations is equal to the square of the intrinsic carrier concentration:

Where:
is the concentration of electrons, approximately equal to .
is the concentration of holes.

Substituting the values:

Calculate :

Now substitute back to find :

Thus, the number density of holes in the doped semiconductor is .

To find the maximum wavelength of light required to produce a hole in a p-type semiconductor, we can use the energy-wavelength relationship of photons, given by the equation:

where:

• is the energy required,
• is Planck's constant ( ),
• is the speed of light ( ),
• is the wavelength.

Given that the acceptor level is situated 50 meV above the valence band, first convert the energy from meV to joules:

Now, solve for :

Simplify the expression:

Thus, the maximum wavelength of light required to produce a hole is , which matches one of the given options.

The correct answer is:

In this problem, we need to identify which V-I graph corresponds to each type of p-n junction diode: forward-biased p-n junction, Zener diode, photodiode, and solar cell. Let's analyze the characteristics of each device to find the correct order:

• Forward-biased p-n junction diode: This will have an exponential V-I relationship where the current increases rapidly after exceeding a threshold voltage (forward voltage).
• Zener diode: Operates in reverse bias, and the V-I graph will show a sharp increase in reverse current after the breakdown voltage is reached.
• Photodiode: Typically operates in reverse bias. The current (reverse current) increases slightly with an increase in reverse voltage. Photocurrent varies with light intensity.
• Solar cell: Operates in the fourth quadrant where light generates a current even when voltage is negative, resembling the graph of a voltage source.

Given these descriptions, let's match with the graph characteristics:

1. The forward-biased p-n junction will have a graph showing a steep rise after a certain positive voltage.
2. The Zener diode’s characteristic curve will show a sharp rise in reverse bias at the breakdown voltage.
3. The photodiode graph will show limited current increase in reverse bias and dependency on light intensity.
4. The solar cell will exhibit characteristics akin to a current generator when exposed to light.

From the options: (D), (C), (A), (B), let's match them:

This matches our analysis, thus the correct answer is: (D), (C), (A), (B).