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The process occurring in the coil-and-capacitor circuit can be compared with the cyclic oscillations of a swinging pendulum, as shown in Figure 26-10 Assume that the electrons in the coil and capacitor are represented by the pendulum s bob The moving bob has the greatest speed at the bottom of its swing, a position at which kinetic energy, KE, is maximized, and potential energy, PE, due to gravity is zero This point in the pendulum s motion, shown in Figure 26-10a, is similar to the peak electric current flow in the coil when the charge on the capacitor is zero When the bob reaches the peak of its swing, its vertical displacement and PE are maximized, whereas its KE is zero because the bob s velocity is zero As shown in Figure 26-10b, this point in the motion is similar to when the capacitor holds the maximum charge and the current through the coil is zero Energy in the coil-and-capacitor circuit As you just learned, the PE of the pendulum is largest when its vertical displacement is greatest, and the KE is largest when the velocity is greatest The sum of the PE and KE the total energy is constant throughout the motion of the pendulum In the coil-and-capacitor circuit, both the magnetic field produced by the coil and the electric field in the capacitor contain energy When the current is largest, the energy stored in the magnetic field is greatest When the current is zero, the electric field of the capacitor is largest, and all the energy is contained in the electric field The total energy of the circuit (the sum of the magnetic field energy, the electric field energy, the thermal losses, and the energy carried away by the generated electromagnetic waves) is constant Energy that is carried, or radiated, in the form of electromagnetic waves is frequently called electromagnetic radiation Just as a pendulum eventually stops swinging if it is left alone, the oscillations in a coil and capacitor die out over time due to resistance in the circuit The oscillations of both systems can be made to continue by adding energy Gentle pushes, applied at the correct times, will keep a pendulum swinging The largest amplitude swings occur when the frequency of pushes matches the frequency of swinging motion This is the condition of resonance, which was discussed in 14 Similarly, voltage pulses applied to the coil-and-capacitor circuit at the right frequency keep the oscillations in the circuit going One way of doing this is to add a second coil to the circuit, to form a transformer A transformer is shown in Figure 26-11 The alternating current induced in the secondary coil is increased by an amplifier and added back to the coil and capacitor This type of circuit can produce frequencies up to approximately 400 MHz.

1 2 3

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Figure 26-10 The motion of a pendulum is analogous to the action of electrons in a coil-andcapacitor circuit Motion of the pendulum s bob is analogous to the current flow in the circuit (a) The point where the pendulum s motion comes to a stop is analogous to zero current in the circuit (b)

Figure 26-1 In a transformer, 1 the amplified oscillation from the secondary coil is in resonance with the coil-and-capacitor circuit and keeps the oscillations going

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