In the network shown below, maximum power is to be transferred to the load \(R_L\). The value of \(R_L\) (in \(\Omega\)) is \(\_\_\_\_\).
In the network shown below, maximum power is to be transferred to the load \(R_L\). The value of \(R_L\) (in \(\Omega\)) is \(\_\_\_\_\).
Correct Answer: 2.5
Solution and Explanation
According to the maximum power transfer theorem, the load resistance \(R_L\) must be equal to the Thevenin resistance \(R_{{Thevenin}}\) of the circuit for maximum power to be delivered to the load: \[ R_L = R_{{Thevenin}}. \] Step 2: Determine \(R_{{Thevenin}}\).
Simplify the given circuit by removing the load and calculating the Thevenin resistance seen across the load terminals. After simplifying, the effective resistance is found to be: \[ R_{{Thevenin}} = 2.5 \, \Omega. \] Final Answer: \[ \boxed{2.5 \, \Omega} \]
Top Questions on Bandwidth
- Let \( X(t) = A \cos(2\pi f_o t + \theta) \) be a random process, where amplitude \( A \) and phase \( \theta \) are independent of each other, and are uniformly distributed in the intervals [−2, 2] and [0, 2π], respectively. \( X(t) \) is fed to an 8-bit uniform mid-rise type quantizer.
Given that the autocorrelation of \( X(\tau) \) is \[ R_x(\tau) = \frac{2}{3} \cos(2\pi f_o \tau), \] the signal to quantization noise ratio (in dB, rounded off to two decimal places) at the output of the quantizer is ___. - Suppose X and Y are independent and identically distributed random variables that are distributed uniformly in the interval [0,1]. The probability that X≥Y is_____.
- In a number system of base r, the equation x2-12x+37=0 has x=8 of its solutions. The value of r is____.
- In the context of Bode magnitude plots, \(40 \, {dB/decade}\) is the same as:
- For the Boolean function: \[ F(A, B, C, D) = \Sigma m(0, 2, 5, 7, 8, 10, 12, 13, 14, 15), \] the essential prime implicants are:
Questions Asked in GATE EC exam
Eight students (P, Q, R, S, T, U, V, and W) are playing musical chairs. The figure indicates their order of position at the start of the game. They play the game by moving forward in a circle in the clockwise direction.
After the 1st round, the 4th student behind P leaves the game.
After the 2nd round, the 5th student behind Q leaves the game.
After the 3rd round, the 3rd student behind V leaves the game.
After the 4th round, the 4th student behind U leaves the game.
Who all are left in the game after the 4th round?
- A full adder and an XOR gate are used to design a digital circuit with inputs \( X, Y, Z \), and output \( F \), as shown below. The input \( Z \) is connected to the carry-in input of the full adder.
If the input \( Z \) is set to logic ‘1’, then the circuit functions as _________ with \( X \) and \( Y \) as inputs.- GATE EC - 2025
- Digital Circuits
Consider a system represented by the block diagram shown below. Which of the following signal flow graphs represent(s) this system? Choose the correct option(s).
- GATE EC - 2025
- Fourier series
- Consider a non-negative function \( f(x) \) which is continuous and bounded over the interval [2, 8]. Let \( M \) and \( m \) denote, respectively, the maximum and the minimum values of \( f(x) \) over the interval. Among the combinations of \( \alpha \) and \( \beta \) given below, choose the one(s) for which the inequality \[ \beta \leq \int_2^8 f(x) \, dx \leq \alpha \] is guaranteed to hold.
- GATE EC - 2025
- Calculus
The following figures show three curves generated using an iterative algorithm. The total length of the curve generated after 'Iteration n' is:
