A 215 ? resistor and a 0.2 H inductor are connected in series with an AC source of 234 V and frequency 106 Hz. (a) What is the current in the circuit? (b) Calculate the phase angle between the current and the voltage of the AC source. I have tried every way possible to find the correct answer, which is a) 0.925A and b) 31.8 degrees, couldn't figure it out. Your help will be greatly appreciated. Thank you!
The voltage around the inductor is 114.5 V rms and L 0.seventy six Henry commencing with this equation: one hundred twenty iR + j(XL)i one hundred twenty (ninety)i + jwLi the place w 2?f 377 for f 60 Hertz The impedance Z R + j377L ninety +j377L The resistor R and the XL of the inductor are at marvelous angles to a minimum of one yet another V inductor ?((one hundred twenty? - Vr?) ?((one hundred twenty? - 36?) 114.5 V rms XL (114.5/36)ninety 286 ohms yet XL 377L so 377L 286 L 0.seventy six Henry
Reactance of inductor (X) is given by X 2πfL X 2 * π * 106 * 0.2 X 133.2 ? Impedance (Z) of circuit: Z √(R? + X?) R 215?; X 133.2 ? Z 252.92 ? Ohm's Law i v/r I 234 / 252.92 I 0.925 A Voltage across R is in phase with the supply voltage, so phase angle arctan(X/R) arctan (133.2 / 215) 31.78°
as easy as having a glass of water XL ω*L 3.1416*2*106*0.2 133.2 ohm Z √R^2+XL^2 √63,968 253 ohm phase angle arccos R/Z arccos(215/253) 0.56 rad 31.8° I V/Z 234/253 0.925 A
