In the circuit shown, the AC voltage source supplies an rms voltage of 115 V and
ID: 1444829 • Letter: I
Question
In the circuit shown, the AC voltage source supplies an rms voltage of 115 V and the circuit has R, = 3.15 k Ohm i and L = 29 mH. At what frequency will the rms current be 33.51 mA (milliamperes)?f = HZ At this frequency, what is the rms potential drop across the resistor? V_ rrrxR = At this frequency, what is the rms potential drop across the inductor? V_ vrmsL= At this frequency, what is the rms potential drop across both the resistor and the inductor combined? V_rmsTotal = What is the average power consumed by the circuit? P avs=Explanation / Answer
impedence Z = ( R2 + XL2 ) 1/2
a.) irms = vrms /Z
XL = L = 2fL
irms = vrms / Z
33.51 x 10-3 = 115 / Z
Z = 115 / 0.03351 = 3431.8114
Z2 = R2 + (2fL )2
2fL = 1361.921247
f = 1361.921247 / 2(0.029) = 7474.3662018 Hz
b.) for R Vrms = Irms x R = 0.03351 x 3150 = 105.5565 Volts
c.) Vrms = Irms x XL = Irms x L = Irms x 2fL = 0.03351 x 2 x 7474.3662018 x 0.029 = 45.63798098 Volts
d.) VrmsTotal = Irms x Z = 0.03351 x 3431.8114 = 115 Volts
e.) before power we need to find phase. = tan-1 ( - XL /R ) = tan-1 ( - 2 x 7474.3662018 x 0.029 / 3150)
= -23.38154093 degrees
Now, power P = VrmsIrms Cos = 115 x 0.03351 x Cos ( -23.38154093) = 3.537198003 Watt