(a) If an RCL series circuit contains a resistance R = 263 W, a capacitance C =

Question

(a) If an RCL series circuit contains a resistance R = 263 W, a capacitance C = 4.5 µF, and an inductance of L = 0.19 H, calculate the inductive reactance XL if the circuit is connected to a voltage source whose frequency is 371 Hz.

(b) Calculate the capacitive reactance XC for the same conditions in part A.

(c) Calculate the impedance Z of the circuit at this frequency.

(d) If the rms voltage across the generator is 141 V, calculate the average power P(at 371 Hz) being used by the circuit.

(e) Calculate the resonant frequency fres of the circuit using the above values for R, L, and C.

(f) Calculate the impedance Zres of the circuit at resonance.

Explanation / Answer

a)

here by using the formula

XL = 2 * pie * f * L

XL = 2 * 3.14 * 371 * 0.19

XL = 442.7 ohm

b)

here the formula is

Xc = 1 / (2 * pie * f * C )

Xc = 1 / ( 2 * 3.14 * 371 * 4.5 * 10^-6)

Xc = 95.4 ohm

c)

then

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

Z = sqrt( 263^2 + ( 442.7 - 95.4)^2 )

Z = 435.6 ohm

d)

the power at 371 Hz is

P = i^2 * R

P = (141 / 435.6)^2 * 263

P = 27.5 watts

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