E-10

Determining the inductance of the inductor For all settings, the inductor has the same resistance R. At different settings, find the absolute value of the impedance ˝Z˝ by useing equation Ve/Ie = ˝Z˝. Inductance can be calculated as L=Ö[(˝Z˝2 - R2)/w2], At different settings, we have different L's. Use those L's to plot L as a function of core setting, which will be used to find the resonance L. Observing series resonance. When you record the current for each setting of the inductor,plot Ie against L(at each setting, you already have their corresponding L). When the brightness of the bulb has the maximum , record L from the graph; this is the resonance L. Use equation w = 1/ÖLC to check your result.(w = 377s-1).

When you study AC theory, the phasor diagram is very important. Be familiar with the phasor diagram. In the circuit with pure resistance, the current and the voltage are in phase just like DC circuit. The resistance depends on the material that the resistor is made of, and will not change due to the frequency. In the circuit with pure inductive reactance(X_L), the current lags the voltage by p/2. In the circuit with pure capacitative reactance(X_C), the current leads the voltage by p/2. In the circuit with RLC, the impedance is calculated as

Z = Ö[R²+(X_L-X_C)²]
The current in the RLC circuit lags the source voltage by j
where j is calculated as
j = tan^-1[(X_L-X_C)/R]

Phasor diagram

When you compare the resonance current with the current in Part 1 with single resistance, you will find that this current is less than the one in part 1. The reason is that the inductor has resistance itself, which contributes to the resistance of the impedance. In the equation Z = Ö [R² + (X_L² - X_C)², R includes two parts, one is the resistance of the resistor, the other one is the resistance of the inductor.

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