Exercise 31.27 You have a 195?? resistor, a 0.397?Hinductor, a 5.03? ? F capacit

Question

Exercise 31.27

You have a 195?? resistor, a 0.397?Hinductor, a 5.03??F capacitor, and a variable-frequency ac source with an amplitude of 2.91V . You connect all four elements together to form a series circuit.

Part A

At what frequency will the current in the circuit be greatest?

? = rad/s  

Part B

What will be the current amplitude at this frequency?

I = A  

Part C

What will be the current amplitude at an angular frequency of 403rad/s ?

I= A

Part D

At this frequency, will the source voltage lead or lag the current?

A)the source voltage leads the current
B)the source voltage lags the current

Explanation / Answer

A)?=1/?(LC)

=707.65 rad/s

B)I=V/Z

V=2.91

Z=?(R^2+(Xl-Xc)^2)

but at this frequency Xl=Xc so Z=R

I=2.91 / 195=0.0149A

C)?=403

Xl=?L=403*0.397=160 ?

Xc=1/(?C)=1/(403*5.03*10^-6)=493.32?

Z=?(195^2+(161.15-489)^2)=386.17 ?

I=2.91 /386.17 =0.0075 A

d) A)the source voltage leads the current

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