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# What is a Resonant Circuit?

A resonant circuit, also known as an LC circuit, tank circuit, or tuned circuit, is a circuit that stores energy and transfers it back and forth repeatedly, similar to a swinging pendulum. The energy passes between an inductor, a circuit component that stores energy in a magnetic field, and a capacitor, which stores energy in an electric field. When the two are working at the same frequency, the circuit is said to be tuned. Such tuning circuits are used in tuners and amplifiers.

The inductor and capacitor work together. The capacitor stores energy in the form of voltage and then releases it in the form of current. The inductor stores energy from the current in its magnetic field and then releases the energy back to the capacitor. The two circuit components pass their stored energy back and forth, a phenomenon called oscillation. The number of times each second that the energy is transferred back and forth is considered the frequency of the resonant circuit.

A resonant circuit is like a pendulum. A person pulls the pendulum to one side, thus storing potential energy, because the pendulum bob is higher than it was before. When the pendulum is released, the potential energy is turned into kinetic energy, the energy of movement. The kinetic energy causes the pendulum to pass through the neutral position to rise on the other side, again storing potential energy. The pendulum oscillates back and forth until it runs out of energy.

Like a pendulum, a resonant circuit works most efficiently when it oscillates at its preferred, or resonant, frequency. The rate at which capacitor and inductor each take up and release energy is a function of time. If one tries to drive the circuit faster than its resonant frequency, either the capacitor or the inductor won’t be able to take up and release the energy fast enough. The circuit's resonance frequency is defined by the equation 1 divided by the square root of L x C. L represents inductance in Henries, and C represents capacitance in Farads.

Like a child on a swing, resonant circuits lose some energy as the energy is passed back and forth, so new energy must be added to keep the circuit going. Wires have resistance. Capacitors don’t release quite as much energy as they take in. The loss in a resonant circuit is measured by the quality factor, or Q factor. A higher Q factor indicates that less energy is lost with each oscillation.

The Q factor is calculated as the ratio of the amplitude, or strength, of oscillations that come out of the circuit, compared to what went into the circuit. A higher Q factor indicates less energy is needed to maintain the circuit and more output is produced for each input. As an analogy, on a child’s swing, this can be compared to how far the swing travels after the parent’s push, compared to how far the parent’s hand traveled while pushing the child.

An oscillator is a special kind of circuit that replaces the energy lost from a less-than-ideal Q factor. When a child pumps a swing at the correct frequency, adding energy to the system at regular intervals to overcome the loss due to friction and wind resistance, the child can swing indefinitely. A radio tuner is a resonant circuit with a high Q factor. Turning the knob changes the capacitance of a variable capacitor. When the resonant circuit is tuned to the same frequency as the radio station transmitter, the circuit produces a high amplitude and clear audio broadcast.

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Why is the total active power of a network always the sum of the individual active powers, regardless of series or parallel connection of components?

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