The free electron concentration profile \(n(x)\) in a doped semiconductor at equilibrium is shown in the figure, where the points A, B, and C mark three different positions. Which of the following statements is/are true?
\begin{center}
\includegraphics[width=8cm]{26.png}
\end{center}
Show Hint
Solution and Explanation
Diffusion currents flow from regions of high electron concentration to regions of low electron concentration. Between points B and C, the electron concentration decreases, causing the diffusion current to flow from C to B. Step 2: Determine the direction of the electric field.
The electric field arises due to the carrier concentration gradient and acts to oppose the diffusion current. Therefore, the electric field direction is from B to C. Final Answer: \[\boxed{{(1), (2), (3)}}\]
Top Questions on ALU
- An NMOS transistor operating in the linear region has \(I_{DS} = 5 \, \mu{A}\) at \(V_{DS} = 0.1 \, {V}\). Keeping \(V_{GS}\) constant, the \(V_{DS}\) is increased to \(1.5 \, {V}\). Given that: \[ \mu_n C_{ox} \frac{W}{L} = 50 \, \mu{A}/{V}^2, \] the transconductance at the new operating point (in \(\mu{A}/{V}\), rounded off to two decimal places) is \(\_\_\_\_\).
- A lossless transmission line with characteristic impedance \(Z_0 = 50 \, \Omega\) is terminated with an unknown load. The magnitude of the reflection coefficient is \(|\Gamma| = 0.6\). As one moves towards the generator from the load, the maximum value of the input impedance magnitude looking towards the load (in \(\Omega\)) is \(\_\_\_\_\).
- In the circuit shown below, the transistors \(M_1\) and \(M_2\) are biased in saturation. Their small signal transconductances are \(g_{m1}\) and \(g_{m2}\), respectively. Neglect body effect, channel length modulation, and intrinsic device capacitances. \begin{center} \includegraphics[width=6cm]{51.png} \end{center} Assuming that capacitor \(C_1\) is a short circuit for AC analysis, the exact magnitude of small signal voltage gain \(\left|\frac{v_{{out}}}{v_{{in}}}\right|\) is \(\_\_\_\_\).
- The sequence of states (\(Q_1 Q_0\)) of the given synchronous sequential circuit is \(\_\_\_\_\). \begin{center} \includegraphics[width=10cm]{42.png} \end{center}
Questions Asked in GATE EC exam
Two resistors are connected in a circuit loop of area 5 m\(^2\), as shown in the figure below. The circuit loop is placed on the \( x-y \) plane. When a time-varying magnetic flux, with flux-density \( B(t) = 0.5t \) (in Tesla), is applied along the positive \( z \)-axis, the magnitude of current \( I \) (in Amperes, rounded off to two decimal places) in the loop is (answer in Amperes).
- GATE EC - 2025
- Faraday's Law
A 50 \(\Omega\) lossless transmission line is terminated with a load \( Z_L = (50 - j75) \, \Omega.\) { If the average incident power on the line is 10 mW, then the average power delivered to the load
(in mW, rounded off to one decimal place) is} _________.- GATE EC - 2025
- Flip-Flop
In the circuit shown below, the AND gate has a propagation delay of 1 ns. The edge-triggered flip-flops have a set-up time of 2 ns, a hold-time of 0 ns, and a clock-to-Q delay of 2 ns. The maximum clock frequency (in MHz, rounded off to the nearest integer) such that there are no setup violations is (answer in MHz).
- GATE EC - 2025
- Flip-Flop
The diode in the circuit shown below is ideal. The input voltage (in Volts) is given by \[ V_I = 10 \sin(100\pi t), \quad {where time} \, t \, {is in seconds.} \] The time duration (in ms, rounded off to two decimal places) for which the diode is forward biased during one period of the input is (answer in ms).
- GATE EC - 2025
- Simple diode circuits
- X and Y are Bernoulli random variables taking values in \( \{0,1\} \). The joint probability mass function of the random variables is given by:
P(X = 0, Y = 0) = 0.06, \( \quad P(X = 0, Y = 1) = 0.14 \), \( \quad P(X = 1, Y = 0) = 0.24 \), \( \quad P(X = 1, Y = 1) = 0.56 \).
The mutual information \( I(X; Y) \) is (rounded off to two decimal places).- GATE EC - 2025
- Information Theory