Total Charge on Sphere Finding Total Charge on a Sphere Basic Formula Q = ∫ ρ dV Given Radius R = 30 cm = 0.3 m Charge density ρ = 200 pC/m³ = 200 × 10 -12 C/m³ Step 1: Volume of Sphere V = (4/3) π R³ V = (4/3) π (0.3)³ V = (4/3) π (0.027) V ≈ 0.113 m³ Step 2: Total Charge Q = ρ × V Q = (200 × 10 -12 ) × 0.113 Q ≈ 22.6 × 10 -12 C Final Answer Q ≈ 2.26 × 10 -11 C Important Note: The solution assumes charge density is constant. If density varies with radius, then: Q = ∫₀ᴿ ρ(r) 4πr² dr

  Costas Receiver Costas Receiver A Costas receiver is a type of phase-locked loop (PLL) system widely used in communication systems for carrier recovery, particularly in suppressed-carrier modulation schemes such as Double Sideband Suppressed Carrier (DSB-SC) and Binary Phase Shift Keying (BPSK). It was invented by John P. Costas and is essential for coherent demodulation. Working Principle The Costas receiver operates by splitting the incoming modulated signal into two separate paths. Each path is mixed with a locally generated carrier signal, but with a 90-degree phase difference between them. These signals are passed through low-pass filters to remove high-frequency components. The outputs are multiplied together to generate an error signal, which a...

  Audio Files: Original vs WAV vs MP3 1. The Original Signal The true original signal is a continuous analog sound wave (air pressure variations over time). That’s what your ears hear. 2. WAV File A .wav file stores audio using Pulse-Code Modulation (PCM) : The analog signal is sampled (measured many times per second) Each sample is quantized into numbers Stored as digital data WAV = digitized version of the original signal, not modulated in the radio sense ✔ Very close to original (especially at high sample rates like 44.1 kHz) 3. MP3 File An .mp3 file uses Perceptual Coding : Starts from PCM audio (like WAV) Removes parts humans are less likely to hear Compresses the data significantly MP3 = compressed and modified version of the original signal ✔ Smaller size ❌ Some information permanen...

  RRAM - Resistive Random Access Memory RRAM (Resistive Random Access Memory) Introduction RRAM is a non-volatile memory technology that stores data by changing the resistance of a material. It is considered a promising candidate for next-generation memory and neuromorphic computing systems. Working Principle RRAM operates based on resistive switching, where the application of voltage causes a change in resistance state. High Resistance State (HRS): Represents binary '0' Low Resistance State (LRS): Represents binary '1' Device Structure Top electrode Resistive switching material (metal oxides / 2D materials) Bottom electrode Key Materials Transiti...

     UGC-NET Electronic Science Question Paper With Answer Key Download Pdf [June 2025] Download Question Paper                   2025 | 2024 | 2023 | 2022 | 2021 | 2020 UGC-NET Electronic Science  June 2025 Answers with Explanations Explanations 1. For forming a p-type semiconductor, the dopant must be a trivalent impurity (three valence electrons) so that it creates acceptor levels and holes become the majority carriers. Among the given elements, boron (B) is a group-III element (trivalent). Arsenic (As) and phosphorus (P) are group-V (pentavalent) donors that produce n-type material, and germanium (Ge) is a group-IV element usually used as the semiconductor, not as an acceptor dopant. Hence, doping an intrinsic semiconductor with B produces a p-type semiconductor. 2. The ohmic resistance of a JFET at zero gate bias is given by the standard relation: R DS(on) = V P / I DSS because ...

Simulator for QPSK Modulation Quadrature (4-PSK) Bitstream (Even length) Carrier Freq (Hz) Samples Per Symbol Run QPSK Simulation The Math Behind QPSK Quadrature Phase Shift Keying (QPSK) is a form of digital modulation that transmits two bits per symbol by changing the phase of a carrier wave. s(t) = A cos(2πf c t + θ n ) Phase (θ n ): Each pair of bits (dibit) corresponds to a specific phase shift. In Gray coding, we use: "00" → π/4 (45°) "01" → 3π/4 (135°) "11" → 5π/4 (225°) "10" → 7π/4 (315°) Efficiency: Since 4 phases are used, QPSK carries double the data of BPSK in the same bandwidth. ...

  BFSK Orthogonality Simulator BFSK Orthogonality Simulator T: f₁: f₂: Run Simulation Signals 📘 Mathematical Model Behind the Simulator The simulator generates two sinusoidal signals used in Binary Frequency Shift Keying (BFSK): s₁(t) = cos(2πf₁t) s₂(t) = cos(2πf₂t) To check orthogonality, it computes the inner product: ∫₀ᵀ s₁(t)s₂(t) dt If the result is approximately zero, the signals are orthogonal. ⚙️ What Each Input Means T (Symbol Duration) This defines the time interval over which signals are observed. Orthogonality depends directly on this value. 0 ≤ t ≤ T f₁ (Frequency 1) Frequency of the first BFSK signal (represents binary "0" or "1"). cos(2πf₁t) f₂ (Frequency 2) ...

  Lumped vs Distributed Circuits Lumped Circuit vs Distributed Circuit The difference between lumped and distributed circuits comes down to how voltage, current, and physical size relate to the signal wavelength. Lumped Circuit Concept: Components are assumed to be concentrated at discrete points. Condition: \[ \text{Size of circuit} \ll \lambda \] Where \( \lambda \) is the wavelength of the signal. Assumptions: Voltage and current are uniform across components No propagation delay Governing Laws: Ohm's Law: \( V = IR \) Kirchhoff’s Laws (KVL and KCL) Examples: DC circuits Low-frequency AC circuits Basic electronic circuits Distributed Circuit Concept: Electrical parameters are distributed continuously along the conductor. Condition: \[ \text{Size of circuit} \approx \lambda \ \text{or larger} \] Characteristics: Voltage and current vary with ...