Impedance Hatching 2 suggests still another function for the transformer. For maximum transfer of energy from an emf device to a resistive load, the resistance of the emf device and the resistance of the load must be equal. The same relation holds for accircuits except that the impedance (rather than just the resistance) of the generator must […]
The Ideal Transformer The transmission rule leads to a fundamental mismatch between the requirement for efficient high-voltage transmission and the need for safe low-voltage generation and consumption. We need a device with which we can raise (for transmission) and lower (for use) the ac voltage in a […]
A Resistive Load shows a circuit containing a resistance element of value R and an ac generator with the alternating. emf of . By the loop rule, we have resistor is connected across an alternating-current generator. (h) The current iR and the potential difference “R across the resistor are plotted on the same graph. both versus time I. They are […]
Forced Oscillations We have seen that once started, the charge, potential difference, and current in both undamped LC circuits and damped RLC circuits (with small enough R) oscillate at angular frequency W Such oscillations are said to be free oscillations (freeof any external emf), and the angular frequency W is said to be the circuit’s natural angular […]
Damped Oscillations In an RLC Circuit A circuit containing resistance, i,inductance, and capacitance is called an RLC circuit. We shall here discuss only series RLC circuits like that shown in With a resistance R present, the total electromagnetic energy U of the circuit (the sum of the electric energy and magnetic energy) is no longer constant; instead, […]
Charge and Current Oscillations Since the differential equations are mathematically identical, their solutions must also be mathematically identical. Because q corresponds to x, we can write the general solution of by analogy to as where Q·is the amplitude of the charge variations, w is the angular frequency of the electro magnetic oscillations, and cjJ is the […]
The LC Oscillator Now let us analyze the oscillations of a resistance less LC circuit, proceeding exactly as we just did for the block-spring oscillator. The total energy V present at any in which UB is the energy stored-in the magnetic field of the inductor and U is the energy stored in the electric field of the capacitor. Since […]
LC Oscillations O uantitatively Here we want to Show explicitly that Eq. 33-4 for the angular frequency of LC oscillations is correct. At the same time, we want to examine even more closely the analogy between LC oscillations and block-spring oscillations. We start by extending somewhat our earlier treatment of the mechanical block-spring oscillator The Block-Spring Oscillator We […]
The Electrical Mechanical Analogy Let us look a little closer at the analogy between the oscillating LC system of and an oscillating block – spring system. Two kinds of energy are involved in the block-spring system. One is potential energy of the compressed or extended spring: the other is kinetic energy of the moving block. […]
New Physics Old Mathematics In this chapter you will see how the electric charge q varies with time in a circuit made up of an inductor L, a capacitor C, and a resistor R. From another point of view, we shall discuss how energy shuttles back and forth.between the magnetic field of the inductor and […]