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# Introduction:You have now seen how resistors and capacitors behave in a circuit with an AC voltage. If set up properly a charge and discharge curve can be observed using an

oscilloscope. Let us now consider adding an inductor, L, in series to the resistor and capacitor. Inductors are a coil of wire that when added to a circuit add some interesting behaviors. Here is a sample circuit diagram of aRIC circuit: Theory:Faraday's Law States that a changing magnetic field induces a non-zero curl electric field. If the magnetic field is changing within a coil of wire, an inductor, we can generate a current within the closed circuit that change by Lenz's law. Alternatively, if we have an AC voltage across aninductor, the component will add additional "resistance" to the circuit by way of Faraday's Law.This is called reactance, usually depicted by a chi, XL. Capacitors also have a reactance, XC. You will see that for AC voltage and current impedance (Z), rather than resistance, is calculated for a circuit. The Impedance is Z=\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}} \ldots(1) X_{L}=\omega L=2 \pi f L \ldots X_{C}=\frac{1}{\omega C}=\frac{1}{2 \pi f C} \ldots(3) and R is the total resistance of the resistor network within the circuit. Q1) What happens to the circuit's impedance, eq(1), when XL=Xc?

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