An RLC series circuit has a 2.7 ohm resistor, a 115 muH inductor, and a 725 muF

Question

An RLC series circuit has a 2.7 ohm resistor, a 115 muH inductor, and a 725 muF capacitor. Find the circuit's impedance, in ohms, at 120 Hz. Find the circuit's impedance, in ohms, at 45 kHz. If the voltage source supplies an rms voltage of 5.68 V, what is the circuit's rms current, in amperes, at a frequency of 120 If the voltage source supplies an rms voltage of 5.68 V, what is the circuit's rms current, in amperes, at a frequency of 45 What is the resonant frequency, in kilohertz, of the circuit? What is the rms current, I_rms, in amperes, at resonance?

Explanation / Answer

a)

here

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

Xc = 1 / ( 2 * 3.14 * 120 * 72.5 * 10^-6)

Xc = 18.3 ohm

then

Xl = 2 * pie * f * L

Xl = 2 * 3.14 * 120 * 115 * 10^-6

Xl = 0.0866 ohm

then impedence is Z = sqrt ( R^2 + ( Xl - Xc)^2 )

Z = sqrt( 2.7^2 + ( 0.0866 - 18.3)^2)

Z = 18.41 ohm

b)

here also we use the same formula

Xc = 1 / ( 2 * 3.14 * 4.5 * 10^3 * 72.5 * 10^-6 )

Xc = 0.488 ohm

then

Xl = 2 * 3.14 * 4.5 * 10^3 * 115 * 10^-6

Xl = 3.25 ohm

then the impedence is

Z = sqrt( 2.7^2 + ( 3.25 - 0.488)^2)

Z = 3.86 ohm

c)

Vrmc = V0 / sqrt2

V0 = 5.68 * sqrt2 = 8.032 volts

then

V = I * Z

8.032 / 18.41 = I

I = 0.436 amp

Irms = 0.436 / sqrt2 = 0.3083 amp

d)

here also

Irms = Vrms / Z

Irms = 5.68 / 3.86 = 1.47 amp

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