Given Values Input voltage: v(t) = 12 sin(ωt) V Load resistance: R = 1 kΩ = 1000 Ω Capacitance: C = 1 μF Inductance: L = 2.2 mH Step 1: Calculate RMS Voltage The peak voltage is V m = 12 V. Hence, V rms = V m / √2 V rms = 12 / √2 V Step 2: Calculate Average Power The average power dissipated in the resistor is P = V rms ² / R P = (12 / √2)² / 1000 P = 144 / 2000 = 0.072 W Step 3: Convert to Milliwatts P = 0.072 × 1000 mW P = 72 mW Final Answer 72.00 mW Average power dissipated in the 1 kΩ load resistance at resonance.

  Find the Output Voltage V o Solve the given circuit using Kirchhoff's Current Law (KCL), Ohm's law, and the supernode method. 1. Given Circuit Parameters Current source 1 mA Resistors 1 kΩ Each resistor Voltage source 6 V Required V o 2. Understand the Circuit The circuit contains a 1 mA current source, four 1 kΩ resistors, and a 6 V source connected between the two midpoint nodes. The output voltage is measured between the top and bottom rails. Reference node Take the bottom rail as ground: 0 V . Let the top rail voltage be V T , and...

Computer Fundamentals Types of Memory and Their Technologies Understand the fundamental relationship between different types of computer memory and the technologies used to implement them. Fundamental Matching Memory type, technology, and key characteristics Memory Type Technology Key Characteristic Cache Memory SRAM Very fast; stores frequently accessed data Main Memory DRAM Holds programs and data currently in use Au...

  Nonlinear Optics One incoming photon is converted into two lower-energy photons, typically in a nonlinear optical medium. Energy is conserved: E in = E 1 + E 2 E in ​ = E 1 ​ + E 2 ​ . Parametric Down-Conversion A nonlinear optical process in which one pump photon is converted into two lower-energy photons, known as the signal and idler photons. 1 Energy Conservation The energy of the pump photon equals the sum of the energies of the signal and idler photons. \[ \boxed{\hbar\omega_p=\hbar\omega_s+\hbar\omega_i} \] \[ \boxed{\omega_p=\omega_s+\omega_i} \] ωₚ Pump angular frequency ...

Passive sensor: Generates its own electrical signal from the measured physical quantity. Example:  A piezoelectric sensor is a passive sensor. Reason: A piezoelectric sensor generates an electrical charge or voltage directly when mechanical pressure, force, or vibration is applied to it. It does not require an external power supply to generate this signal. A piezoelectric sensor used to detect vibration in a machine. Therefore, a piezoelectric sensor is classified as a passive transducer because it converts mechanical energy into electrical energy directly. Active sensor: Requires external excitation or power to operate, such as an RTD (which requires a measuring current).

  Q. A binary ripple counter is designed to count  (0)₁₀ to (64)₁₀ . Which of the following is/are the number of flip-flops required to design the counter?   (A) 6 (B) 7 (C) 4 (D) 5 Solution A binary ripple counter must count from (0)₁₀ to (64)₁₀ , including both endpoints. Step 1: Calculate the total number of states Since both 0 and 64 are included, add 1 to the difference: N = Last value − First value + 1 N = 64 − 0 + 1 = 65 states The counter visits every integer from 0 through 64: 0, 1, 2, 3, ..., 63, 64 There are 65 distinct states in total. Step 2: Calculate the number of flip-flops Each flip-flop stores one bit. With n flip-flops, the counter can represent 2ⁿ distinct states. 2⁶ = 64 states (not enough) 2⁷ = 128 states (eno...

Q. An S-band radar transmitting at 3 GHz radiates 200 kW of power. Determine the signal power density at a range of 100 nautical miles if the effective area of the radar antenna is 9 m². Solution Given, Transmitted power: P t = 200 kW = 200,000 W Frequency: f = 3 GHz = 3 × 10⁹ Hz Range: R = 100 nautical miles Effective antenna area: A e = 9 m² Speed of light: c = 3 × 10⁸ m/s Step 1: Convert Nautical Miles to Meters One nautical mile equals 1852 meters. R = 100 × 1852 = 185200 m Step 2: Calculate the Wavelength The wavelength is calculated using the relationship between the speed of light and frequency: λ = c / f λ = (3 × 10⁸) / (3 × 10⁹) λ = 0.1 m Step 3: Calculate the Antenna Gain The relationship between effective aperture and antenna gain is: G = (4πAₑ) / λ² ...

  Q. The electric field of a monochromatic plane wave travelling in a lossless isotropic and homogenous medium is given by E(z, t) = E₀ [x̂ cos(ωt − kz) + ŷ sin(ωt − kz)] in a right-handed orthogonal co-ordinate system. Which of the following is the correct polarization of the electromagnetic wave? (A) Right-handed circularly polarized Correct answer under the IEEE convention. (B) Left-handed circularly polarized (C) Linearly polarized (D) Linearly polarized at −45° to x̂ Solution 1. Identify the electric-field components Let ψ = ωt − kz. The components along the x and y directions are: Eₓ = E₀ cos ψ Eᵧ = E₀ sin ψ Both components have equal amplitudes, the same frequency, and a phase difference of 90°. These are the conditions for circular polarization. ...