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We start with an idealized circuit of zero resistance that contains an inductor and a capacitor, an LC circuit. When the switch is closed, the capacitor begins to discharge, producing a current in the circuit. The current, in turn, creates a magnetic field in the inductor.

The decay of current and voltage transients in RC and RL circuits is caused by energy dissipation in the resistor. In contrast, an LC circuit, which has a capacitor connected to an inductor, ideally has no resistance or energy loss, and exhibits very different behavior.

Finally, the current in the LC circuit is found by taking the time derivative of q(t): i(t)=dq(t)dt=−ωq0sin(ωt+ϕ).Nov 5, 2020

So putting these facts together we can conclude that given an AC series current the voltages across any L and C must have a phase difference of 180˚.

Resonant frequency of a LC circuit is 10 kHz.

• Thus at resonant condition when total electrical impedance Z will be zero means X L and X C cancel out each other. hence, current supplied to a series LC circuit is maximum ( ). Therefore the series LC circuit, when connected in series with the load, will act as a band-pass filter having zero impedance at the resonant frequency.

• A series resonant LC circuit is used to provide voltage magnification. A parallel resonant LC circuit is used to provide current magnification and also used in the RF amplifier circuits as the load impedance, the amplifier’s gain is maxed at the resonant frequency.

• Transient Current in an LC circuit with a DC supply. Here is a LC circuit with a DC supply. When the switch is closed at t=0 capacitor behaves as a short circuit while the inductor behaves as an open circuit as the voltage across the inductor immediately jumps to battery voltage.

• The applications of these circuits mainly involve in transmitters, radio receivers, and TV receivers. Consider an LC circuit in which capacitor and inductor both are connected in series across a voltage supply. The connection of this circuit has a unique property of resonating at a precise frequency termed as the resonant frequency.

To design Series LC circuit and find out the current flowing thorugh each component. Inductance, Capacitor, AC power source, ammeter, voltmeter, connection wire etc.. The schematic diagram below shows an ideal series circuit containing inductance and capacitance but no resistance.

Thus at resonant condition when total electrical impedance Z will be zero means X L and X C cancel out each other. hence, current supplied to a series LC circuit is maximum ( ). Therefore the series LC circuit, when connected in series with the load, will act as a band-pass filter having zero impedance at the resonant frequency.

A series resonant LC circuit is used to provide voltage magnification. A parallel resonant LC circuit is used to provide current magnification and also used in the RF amplifier circuits as the load impedance, the amplifier’s gain is maxed at the resonant frequency.

At that instant the current is changing at the rate of: An LC circuit has a capacitance of 30 µF and an inductance of 15 mH. At time t = 0 the charge on the capacitor is 10 µC and the current is 20 mA. The maximum current is: An RLC circuit has a resistance of 200 Ω and an inductance of 15 mH. Its oscillation frequency is 7000 Hz.