A 404-? resistor, an inductor, and a capacitor are in series with an AC source.

Question

A 404-? resistor, an inductor, and a capacitor are in series with an AC source. The reactance of the inductor is 701 ?, and the circuit impedance is 759 ?.

(a) What are the possible values of the reactance of the capacitor?

(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?

(c) Repeat part (a) assuming the resistance is 202 ? instead of 404 ? and the circuit impedance continues to be759 ?.

A 404-? resistor, an inductor, and a capacitor are in series with an AC source. The reactance of the inductor is 701 ?, and the circuit impedance is 759 ?. (a) What are the possible values of the reactance of the capacitor? (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? (c) Repeat part (a) assuming the resistance is 202 ? instead of 404 ? and the circuit impedance continues to be759 ?.

Explanation / Answer

a)

Impedance

Z=sqrt[R2+(XL-XC)2]

7592=[4042+(701-XC)2]

701-XC=(+ or -)642.5

Case 1:

701-XC=642.5

XC=58.5 ohms

Case 2:

701-XC=-642.5

XC=1343.5 ohms

b)

XC=58.5 ohms

c)

Impedance

Z=sqrt[R2+(XL-XC)2]

7592=[2022+(701-XC)2]

701-XC=(+ or -)731.6

Case 1:

701-XC=731.6

XC=-30.6 ohms( which will not be possible)

Case 2:

701-XC=-731.6

XC=1432.6 ohms (which is the only value)

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