Question
In a p-n junction diode, the current I can be expressed as,
$I=I_0\ \text{exp}\Big(\frac{\text{eV}}{2\text{k}_{\text{B}}\text{T}}-1\Big)$
where $I_0$ is called the reverse saturation current, V is the voltage across the diode and is positive for forward bias and negative for reverse bias, and $I$ is the current through the diode, $k_g$ is the Boltzmann constant $(8.6\times 10^{-5} eV/K)$ and T is the absolute temperature. If for a given diode $I_0 = 5\times 10^{-12} A$ and $T = 300 K$, then,
  1. What will be the forward current at a forward voltage of 0.6V?
  2. What will be the increase in the current if the voltage across the diode is increased to 0.7V?
  3. What is the dynamic resistance?
  4. What will be the current if reverse bias voltage changes from 1V to 2V?

Answer

In a p-n junction diode, the expression for current is given as:
$I=I_0\ \text{exp}\Big(\frac{\text{eV}}{2\text{k}_{\text{B}}\text{T}}-1\Big)$
Where,
$I_0$ = Reverse saturation current $= 5 \times 10^{-12} A$
$T =$ Absolute temperature $= 300K$
$k_B= $ Boltzmann constant $= 8.6 \times 10^{-5} eV/K = 1.376 \times 10^{-23} J K ^{-1}$
V = Voltage across the diode
  1. Forward voltage, V = 0.6 V
$\therefore\text{Current,}\ I=5\times10^{-12}\Bigg[\text{exp}\Bigg(\frac{1.6\times10^{-19}\times0.6}{1.376\times10^{-23}\times300}\Bigg)-1\Bigg]$
$= 5 \times 10^{-12} \times$ exp $[22.36] = 0.0256 A$
Therefore, the forward current is about 0.0256 A.
  1. For forward voltage, V = 0.7 V, we can write:
$I=5\times10^{-12}\Bigg[\text{exp}\Bigg(\frac{1.6\times10^{-19}\times0.7}{1.376\times10^{-23}\times300}-1\Bigg)\Bigg]$
$= 5 \times 10^{-12} \times$ exp $[26.25] = 1.257 A$
Hence, the increase in current, $\Delta{I}=I'-I$
= 1.257 - 0.0256 = 1.23 A
$\text{Dynamic resistance }=\frac{\text{Change in voltage}}{\text{Change in current}}$
  1. Dynamic resistance
$=\frac{0.7-0.6}{1.23}=\frac{0.1}{1.23}=0.081\Omega$
  1. If the reverse bias voltage changes from 1V to 2V, then the current $I$ will almost remain equal to $I_0$ in both cases. Therefore, the dynamic resistance in the reverse bias will be infinite.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

Find an expression for the electric field strength at a distant point situated (i) on the axis and (ii) along the equatorial line of an electric dipole.
OR
Derive an expression for the electric field intensity at a point on the equatorial line of an electric dipole of dipole moment $\vec{\text{p}}$ and length 2a. What is the direction of this field?
The half-li fe of $^{199}Au$ is 2.7  days.
  1. Find the activity of a sample containing $1.00\mu\text{g}$ of $^{198}Au.$
  2. What will be the activity after 7 days? Take the atomic weight of $^{198}Au$ to be 198g/mol.
A magnetic field in a certain region is given by $\text{B}=\text{B}_0\cos(\omega\text{t})\hat{\text{k}}$ and a coil of radius a with resistance R is placed in the x-y plane with its centre at the origin in the magnetic field (see Fig). Find the magnitude and the direction of the current at (a, 0, 0) at $\text{t}=\frac{\pi}{2\omega},\text{t}=\frac{\pi}{\omega} \text{ and }\text{t}=\frac{3\pi}{2\omega}$.
A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. The width of each stair is a and the height is b. Find the capacitance of the assembly.
A closed circular wire hung on a nail in a wall undergoes small oscillations of amplitude $2^0 $ and time period 2s. Find,
  1. The radius of the circular wire,
  2. The speed of the particle farthest away from the point of suspension as it goes through its mean position,
  3. The acceleration of this particle as it goes through its mean position and
  4. The acceleration of this particle when it is at an extreme position. Take $\text{g}=\pi^2\text{m/s}^2.$
The earth revolves round the sun due to gravitational attraction. Suppose that the sun and the earth are point particles with their existing masses and that Bohr's quantization rule for angular momentum is valid in the case of gravitation. (a) Calculate the minimum radius the earth can have for its orbit. (b) What is the value of the principal quantum number n for the present radius? Mass of the earth $= 6.0 \times 10^{-24}kg$. Mass of the sun $= 2.0 \times 10^{30}kg, $ earth-sun distance $= 1.5 \times 10^{11}m.$
A car is speeding up on a horizontal road with an acceleration a. Consider the following situations in the car.
  1. A ball is suspended from the ceiling through a string and is maintaining a constant angle with the vertical. Find this angle.
  2. A block is kept on a smooth incline and does not slip on the incline. Find the angle of the incline with the horizontal.
A parallel-plate capacitor having plate area $400cm^2$ and separation between the plates 1.0mm is connected to a power supply of 100V. A dielectric slab of thickness 1.0mm and dielectric constant 5.0 is inserted into the gap:
  1. Find the increase in electrostatic energy.
  2. If the power supply is now disconnected and the dielectric slab is taken out, find the further increase in energy.
  3. Why does the energy increase in inserting the slab as well as in taking it out?
The benches of a gallery in a cricket stadium are 1m wide and 1m high. A batsman strikes the ball at a level one metre above the ground and hits a mammoth sixer. The ball starts at 35m/s at an angle of 53° with the horizontal. The benches are perpendicular to the plane of motion and the first bench is 110m from the batsman. On which bench will the ball hit?
A parallel-plate capacitor of capacitance $5\mu\text{F}$ is connected to a battery of emf 6V. The separation between the plates is 2mm:
  1. Find the charge on the positive plate.
  2. Find the electric field between the plates.
  3. A dielectric slab of thickness 1mm and dielectric constant 5 is inserted into the gap to occupy the lower half of it. Find the capacitance of the new combination.
  4. How much charge has flown through the battery after the slab is inserted?