A series RCL circuit has a resonant frequency of 1530 Hz. When operating at a fr

Question

A series RCL circuit has a resonant frequency of 1530 Hz. When operating at a frequency other than 1530 Hz, the circuit has a capacitive reactance of 5.0 ohms and an inductive reactance of 31.0 ohms.

(a) What is the value of L? (in units of H)

(b) What is the value of C? (in units of F)

A series RCL circuit has a resonant frequency of 1530 Hz. When operating at a frequency other than 1530 Hz, the circuit has a capacitive reactance of 5.0 ohms and an inductive reactance of 31.0 ohms. (a) What is the value of L? (in units of H) (b) What is the value of C? (in units of F) A 2600 omega resistor and a 1.1 muF capacitor are connected in series across a generator (60.0 Hz, 120 V rms). Determine the average power dissipated in the circuit.

Explanation / Answer

XL = 2pifL = 31

L   = 31/(2*3.14*1530)

L = 3.22*10^-3   Henry

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XC = 1/2pifC = 5

C = 1/(2*3.14*1530 * 5)

C = 20.81 *10^-6 Farads

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Xc = 1/(2*3.14* 60* 1.1e-6) = 2412.66 ohms

so Z^2 = R^2+(Xc)^2

Z^2 = 2600^2 + 2412.66^2

Z = 3546.96 ohms

power facrtor cos theta = R/Z = 2600/3546.96 =0.733

so AVg Power = V^2/R cos theta

Power = 120*120* 0.733/2600

P = 4.05 watts

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