A 394-? resistor, an inductor, and a capacitor are in series with an AC source.

Question

A 394-? resistor, an inductor, and a capacitor are in series with an AC source. The reactance of the inductor is 696 ?, and the circuit impedance is 754 ?.

(a) What are the possible values of the reactance of the capacitor? (Enter your answers from smallest to largest. Enter NONE in any unused answer boxes.) ?

1)

2)

(b) If you find that the power delivered to the circuit decreases as you raise the frequency, what is the capacitive reactance in the original circuit?

1)

(c) Repeat part (a) assuming the resistance is 197 ? instead of 394 ? and the circuit impedance continues to be 754 ?.

1)

2)

Explanation / Answer

a)

Impedance

Z=sqrt[R^2+(XL-Xc)^2

754^2=sqrt[394^2+(696-Xc)^2]

(696-Xc)^2=413,280

696-Xc=(+ or -)642.9 ohms

case1

696-Xc=642.9

Xc=53.1 ohms (smallest)

case 3

696-Xc=-642.9

Xc=1338.9 ohms=1338 ohsm (approx) (largest)

b)

as frequency is increases ,capacitive reactacne decreases ,so

Xc=53.1 ohms

c)

754 =sqrt[197^2+(696-Xc)^2]

696-Xc=(+ or -)727.8

case 1:

696-Xc=727.8

Xc=-31.8 ohms (which was not possible)

case 2:

696-Xc=-727.8

Xc=1423.8 ohms

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