Each of the resistance shown in figure (45-E2) has a value of
Question: Each of the resistance shown in figure (45-E2) has a value of $20 \Omega$. Find the equivalent resistance between A and B. Does it depends on whether the point $\mathrm{A}$ or $\mathrm{B}$ is at higher potential? Solution:...
Read More →Calculate the current through the circuit and the potential difference across
Question: Calculate the current through the circuit and the potential difference across the diode shown in figure (45-E1). The drift current for the diode is $20 \mu \mathrm{A}$. Solution:...
Read More →Solve this following
Question: Evaluate: i. $\int \frac{\tan x}{(\sec x+\tan x)} d x$ ii. $\int \frac{\operatorname{cosec} x}{(\operatorname{cosec} x-\cot x)} d x$ Solution:...
Read More →Consider a p-n junction diode having the characteristic
Question: Consider a p-n junction diode having the characteristic $\mathrm{i}=\mathrm{i}_{0}\left(\mathrm{e}^{\mathrm{ev} / \mathrm{kT}-1)}\right.$ Where $\mathrm{i}_{0}=20 \mu \mathrm{A}$. The diode is operated at $\mathrm{T}=300 \mathrm{~K}$. (a) Find the current through the diode when a voltage of $300 \mathrm{mV}$ is applied across it in forward bias. (b) At what voltage does the current double? Solution:...
Read More →Solve this following
Question: Evaluate: i. $\int \frac{1}{(1-\cos x)} d x$ ii. $\int \frac{1}{(1-\sin x)} d x$ Solution: $=\tan x+\sec x+c$...
Read More →The current-voltage characteristic of an ideal p-n junction diode is given by
Question: The current-voltage characteristic of an ideal p-n junction diode is given by $\mathrm{i}=\mathrm{i}_{0}\left(\mathrm{e}^{\mathrm{ev} / \mathrm{kT}}-1\right)$ Where the drift current $\mathrm{i}_{0}$ equals $10^{\mu \mathrm{A}}$. A take the temperature $T$ to be $300 \mathrm{~K}$. (a) Find the voltage $\mathrm{V}_{0}$ for which $\mathrm{e}^{\mathrm{ev} / \mathrm{kT}}=100$. One can neglect the term 1 for voltages greater than this value. (b) Find an expression for the dynamic resistance...
Read More →Solve this following
Question: Evaluate: i. $\int(\tan x+\cot x)^{2} d x$ ii. $\int\left(\frac{1+2 \sin x}{\cos ^{2} x}\right) d x$ iii. $\int\left(\frac{3 \cos x+4}{\sin ^{2} x}\right) d x$ Solution: i. Given:...
Read More →The drift current in a p-n junction is 20.0μA
Question: The drift current in a p-n junction is $20.0 \mu \mathrm{A}$ Estimate the number of electrons crossing a cross-section per second in the depletion region. Solution:...
Read More →When a p-n junction is reverse-biasedn the current becomes almost constant
Question: When a p-n junction is reverse-biasedn the current becomes almost constant at $25 \mu \mathrm{A}$. When it is forward-biased at $200 \mathrm{mV}$, a current of $75 \mu \mathrm{A}$ is obtained. Find the magnitude of diffusion current when the diode is (a) unbiased, (b) reverse-baised at $200 \mathrm{mV}$ and (c) forward-baised at $200 \mathrm{mV}$. Solution:...
Read More →In a p-n junction, a potential barrier of 250meV
Question: In a p-n junction, a potential barrier of $250 \mathrm{meV}$ exists across the junction. A hole with a kinetic energy of $300 \mathrm{meV}$ approaches the junction. Find the kinetic energy of the hole when it crosses the junction if the hole approached the junction (a) from the p-side and (b) from the n-side. Solution:...
Read More →Solve this following
Question: Evaluate: i. $\int \sec x(\sec x+\tan x) d x$ ii. $\int \operatorname{cosec} x(\operatorname{cosec} x-\cot x) d x$ Solution:...
Read More →The potential barrier existing across an unbiased p-n junction is
Question: The potential barrier existing across an unbiased p-n junction is $0.2$ volt. What minimum kinetic energy a hole should have to diffuse from the p-side to the $n$-side if (a) the junction is unbiased, (b) the junction is forward biased at $0.1$ volt and (c) the junction is reverse-biased at $0.1$ volt? Solution:...
Read More →Solve this following
Question: Evaluate: $\int\left(\frac{\cot x}{\sin x}-\tan ^{2} x-\frac{\tan x}{\cos x}+\frac{2}{\cos ^{2} x}\right) d x$ Ans. $-\operatorname{cosec} x+\tan x+x-\sec x+C$ Solution:...
Read More →In a p-n junction, the depletion region is
Question: In a p-n junction, the depletion region is $400 \mathrm{~nm}$ wide and an electric field of $5 \times 10^{5} \mathrm{~V} / \mathrm{m}$ exists in it. (a) Find the height of the potential barrier. (b) What should be the minimum kinetic energy of a conduction electron which can diffuse from the n-side to the p-side? Solution:...
Read More →A semiconductor material has a band gap of 1eV.
Question: A semiconductor material has a band gap of 1eV. Acceptor impurities are doped into it which create acceptor levels 1 meV above the valence band. Assume that the transition from one energy level to the other is almost forbidden if $k T$ is less than $1 / 50$ of the energy gap. Also, if $k T$ is more than twice the gap. The upper levels have maximum population. The temperature of the semiconductor is increased from oK. The concentration of the holes increases with temperature and after a...
Read More →Solve this following
Question: Evaluate: $\int\left(9 \sin x-7 \cos x-\frac{6}{\cos ^{2} x}+\frac{2}{\sin ^{2} x}+\cot ^{2} x\right) d x$ Solution:...
Read More →The conductivity of an intrinsic semiconductor depends on temperature as
Question: The conductivity of an intrinsic semiconductor depends on temperature as $\sigma=\sigma_{0} \mathrm{e}^{-\Delta \mathrm{E} / 2 \mathrm{kT}}$ where $\sigma_{0}$ is a constant. Find the temperature at which the conductivity of an intrinsic germanium semiconductor will be double of its value at $\mathrm{T}=300 \mathrm{~K}$. Assume that the gap for germanium is $0.650 \mathrm{eV}$ and remains constant as the temperature is increased. Solution:...
Read More →The product of the hole concentration and the conduction electron concentration
Question: The product of the hole concentration and the conduction electron concentration turns out to be independent of the amount of any impurity doped. The concentration of conduction electrons in germanium is $6 \times 10^{19}$ per cubic metre. When some phosphorus impurity is droped into a germanium sample, the concentration of conduction electrons increases to $2 \times 10^{23}$ per cubic metre. Find the concentration of the holes in the doped germanium. Solution:...
Read More →Solve this following
Question: Evaluate: i. $\int\left(\frac{x^{2}-1}{x^{2}+1}\right) d x$ ii. $\int\left(\frac{x^{6}-1}{x^{2}+1}\right) d x$ iii. $\int\left(\frac{x^{4}}{1+x^{2}}\right) d x$ iv. $\int\left(\frac{x^{2}}{1+x^{2}}\right) d x$ Solution:...
Read More →Estimate the proportion of boron impurity which will increase the conductivity
Question: Estimate the proportion of boron impurity which will increase the conductivity of a pure silicon sample by a factor of $100 .$ Assume that each boron atom creates a hole and the concentration of holes in pure silicon at the same temperature is $7 \times 10^{16}$ holes per cubic metre. Density of silicon is $5 \times 10^{28}$ atoms per cubic metre. Solution:...
Read More →The conductivity of a pure semiconductor is roughly proportional to
Question: The conductivity of a pure semiconductor is roughly proportional to $\mathrm{T}^{3 / 2} \mathrm{e}^{-\Delta \mathrm{E} / 2 \mathrm{kT}}$ where $\Delta \mathrm{E}_{\text {is }}$ the band gap. The band gap for germanium is $0.74 \mathrm{eV}$ at $4 \mathrm{k}$ and $0.67 \mathrm{eV}$ at $300 \mathrm{k}$. By what factor does the conductivity of pure germanium increase as the temperature is raised from $4 \mathrm{~K}$ to $300 \mathrm{~K}$ ? Solution:...
Read More →Solve this following
Question: Evaluate: $\int\left[1+\frac{1}{\left(1+x^{2}\right)}-\frac{2}{\sqrt{1-x^{2}}}+\frac{5}{x \sqrt{x^{2}-1}}+a^{x}\right] d x$ Solution:...
Read More →Let ΔE denote the energy gap between the valence band and the conduction band.
Question: Let $\Delta \mathrm{E}$ denote the energy gap between the valence band and the conduction band. The population of conduction electrons (and of the holes) is roughly proportional to $\mathrm{e}^{-\Delta \mathrm{E} / 2 \mathrm{kT}}$. Find the ratio of the concentration of conduction electrons in diamond to that in silicon at room temperature $300 \mathrm{~K} . \Delta \mathrm{E}$ for silicon is $1.1 \mathrm{eV}$ and for diamond is $6.0 \mathrm{eV}$. How many conduction electrons are likel...
Read More →In a photoiode, the conductivity increases when the material is exposed to light.
Question: In a photoiode, the conductivity increases when the material is exposed to light. It is found the conductivity changes only if the wavelength is less than $620 \mathrm{~nm}$. What is the band gap? Solution:...
Read More →Solve this following
Question: Evaluate: i. $\int\left(x^{2}-\frac{1}{x^{2}}\right)^{3} d x$ ii. $\int\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right) d x$ iii. $\int\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)^{2} d x$ iv. $\int \frac{(1+2 x)^{3}}{x^{4}} d x$ v. $\int \frac{(1+x)^{3}}{\sqrt{x}} d x$ vi. $\int \frac{2 x^{2}+x-2}{(x-2)} d x$ Solution:...
Read More →