Does the source voltage lead or lag the current? Calculate the voltage amplitude

Question

Does the source voltage lead or lag the current?

Calculate the voltage amplitude across the capacitor.

Give your answer in volts, and state only the magnitude.

Determine the power factor of the circuit.

Find the average power delivered to the entire circuit.

Give your answer in Watts.

Determine the average power delivered to the capacitor.

Give your answer in Watts

Calculate the resonance angular frequency of the circuit.

Give your answer in radians per second.

A resistor R, 155.0 2, an inductor, L, 0.290 H, a capacitor C,-7.30 uF, and a voltage source with V- 30.0 V and w 330.0 rads/s are connected in series. Use this circuit to answer all questions Find the impedance of the circuit, in ohms. Answer: Determine the current amplitude, in mA. Answer: Determine the phase angle of the source voltage with respect to the current. Give your answer as a whole number of degrees, in the range -90 to 90

Explanation / Answer

R = 155 ohm

xL = w L = 330 x 0.290 = 95.7 ohm

xC = 1/wC = 415.1 ohm

Impedance, Z = sqrt[ R^2 + (XL - XC)^2]

Z = 355 ohm .....Ans

I = V / Z = 30 / 355

I = 0.0845 A Or 84.5 mA  

Ans: 84.5 mA

phase angle, phi = tan^-1[(XL - XC)/R]

phi = - 64 deg .....Ans

voltage lag current.

Vc = I Xc = 35.1 Volt ....Ans

power factor = cos(phi) =0.44 .....Ans

P_avg = Irms^2 R = I^2 R / 2 = 0.55 W ....Ans

P_avg for capacitor = 0 ....Ans

f0 = 1/(2 pi sqrt(LC)) = 109 Hz ....Ans

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