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Question #108875
1.

A 400 mH coil of negligible resistance is connected to an AC circuit in which an effective current of 6 mA is flowing. Find out the voltage across the coil if the frequency is 1000 Hz.

2.

A capacitor of capacitance 102/π µF is connected across a 220 V, 50 Hz A.C. mains. Calculate the capacitive reactance, RMS value of current and write down the equations of voltage and current.

3.

Find the impedance of a series RLC circuit if the inductive reactance, capacitive reactance and resistance are 184 Ω, 144 Ω and 30 Ω respectively. Also calculate the phase angle between voltage and current.
1
2020-04-10T13:40:03-0400

1) The voltage can be found by Ohm's law:

"V=IX_L=I\\omega L=I\\cdot2\\pi fL=15\\text{ V}."

2) The capacitive reactance is

"X_C=\\frac{1}{2\\pi fC}=98\\space\\Omega."

RMS value of current:

"I=\\frac{V}{X_C}=2.2\\text{ A}."

3) The impedance of a series RLC circuit is

"Z=\\sqrt{(X_L-X_C)^2+R^2}=50\\space\\Omega."

The phase angle between voltage and current equals

"\\phi=\\text{atan}\\frac{X_L-X_C}{R}=53^\\circ."

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