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23.1 Introduction In this chapter, we will explore RL (resistor-inductor) and LC (inductor-capacitor) circuits. These circuits are essential to understanding the transient behavior and oscillations that occur in various electrical and electronic applications. 23.2 RL Circuits An RL circuit consists of a resistor and an inductor connected in series. When a voltage is applied across…

24.1 Introduction In this chapter, we will explore LRC series circuits, which combine resistors inductors and capacitors in series. These circuits are critical in various applications, including filters, oscillators, and transient suppression. 24.2 The LRC Series Circuit An LRC series circuit consists of a resistor an inductor and a capacitor connected in series. The response…

22.1 Introduction In this chapter, we will explore the concept of mutual inductance, which describes how the magnetic field generated by one coil affects another nearby coil. Mutual inductance plays an essential role in understanding transformers, which are used to convert alternating current (AC) voltages and currents in various applications, such as power transmission. 22.2…

Introduction A laser (Light Amplification by Stimulated Emission of Radiation) is a device that generates a beam of coherent light. The properties of laser light – monochromaticity, coherence, and directionality – differentiate it from other light sources like lamps or LEDs. Lasers find a broad spectrum of applications, from scientific research and medicine to data…

Problem 9.2 An alternative derivation of the WKB formula (Equation 9.10) is based on an expansion in powers of . Motivated by the free-particle wave function, we write where is some complex function. (Note that there is no loss of generality here—any nonzero function can be written in this way.) (a) Put this into Schrödinger’s…

17.1 Introduction In this chapter, we will discuss the principles behind the operation of direct-current (DC) motors. These motors convert electrical energy into mechanical energy by generating torque through the interaction of electric currents and magnetic fields. 17.2 Structure of a DC Motor A DC motor consists of two main components: the stator and the…

Introduction The Fizeau experiment, conducted by French physicist Armand Fizeau in 1851, was one of the first direct measurements of the speed of light. Fizeau’s method was ingenious and had a significant impact on the development of theories regarding the nature of light and its propagation. Experimental Setup Fizeau directed a beam of light at…

Problem 8.2 Find the best bound on for the one-dimensional harmonic oscillator using a trial wave function of the form where is determined by normalization and is an adjustable parameter. Solution: Problem 8.2 Solution (Download)

Overview Named after the German mathematician Emmy Noether, Noether’s theorem is a fundamental theorem in theoretical physics and the calculus of variations. It relates symmetries in physical systems to conservation laws, providing a deep insight into the structure of physical laws. Basic Statement of Noether’s Theorem In its simplest form, Noether’s theorem states that for…

Introduction Pions, also known as pi mesons, are a type of subatomic particle in the meson family. They were first proposed in 1935 by Japanese physicist Hideki Yukawa as a particle mediator for the strong nuclear force that holds protons and neutrons together in the atomic nucleus. Basic Properties of Pions Pions come in three…