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Alternating Currents: LRC circuits, resonance

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An L-R-C series circuit is connected to an AC source of constant voltage amplitude V and variable angular frequency w.

A) Show that the current amplitude, as a function of w

See Eq 1

B) Show the average power dissipated in the resistor

See Eq 2

C) Show that I and P are both maximum when the source frequency equals the resonance frequency of the circuit.

See Eq 3

D) Graph P as a function of for V=100V, R=200 ohms, L=2 H, and C= 0.5 micro F. Discuss the behavior of I and P in the limits w=0 w-->infinity

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Four parts about LRC circuits are solved and explained.

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LRC series circuit 5
An L-R-C series circuit is connected to an AC source of constant voltage amplitude V and variable angular frequency w.

A) Show that the current amplitude, as a function of w

See Eq 1
The Net oppose to the current in an A.C. circuit is not only due to the resistance but due to the inductance and capacitance as well. As there is no loss of energy against the inductance and capacitance their oppose to the current is called reactance. The reactance depends on the frequency of the current. If the angular frequency of the source is w then
The inductive reactance is given as and
The capacitive reactance is given by
The current at any instant in the circuit I remain same through the circuit. The voltage across the inductor is ahead in phase then current by 900 and lagging behind by 900 across the capacitor. ...

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