An L - R - C series circuit is constructed using a 175? resistor, a 12.5 ? F cap

Question

An L -R -C series circuit is constructed using a 175? resistor, a 12.5?F capacitor, and an 8.00-mH inductor, all connected across an ac source having a variable frequency and a voltage amplitude of 25.0 V .

a)At what angular frequency will the impedance be smallest?

b)What is the impedance at this frequency?

c)At the angular frequency in part A, what is the maximum current through the inductor?

d)At the angular frequency in part A, find the potential difference across the ac source, the resistor, the capacitor, and the inductor at the instant that the current is equal to one-half its greatest positive value.

Thanks!

Explanation / Answer

a) impedence will be smallest at resonance
i.e XL=Xc
=> w=1/sqrt(LC)
w=3162.27

b) Net impedence=resistance of circuit
=175ohms

c) I=25/175==1/7=0.142857A

d)potential difference across Ac source=12.5V
across resistor=12.5V

across inductor: 0.142857*(3162.27*8mH)j/2=1.807jV
across capacitor=-1.807jV

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