A coil having a resistance of 7 Ω and an inductance of 31.8 mH is connected to a 230V, 50Hz supply. Calculate (a) the circuit current (b) the phase angle (c) the power factor. (d) power consumed. Ans (18.85, 55° lag, .573° lag, 2484.24 w)
Data Given:
Resistance of the coil = R = 7 Ω
Inductance = L = 31.8 mH = 31.8 x10⁻³ H
Frequency of A.C. supply = f = 50 Hz
Voltage (rms) = VrmsVrms = 230 V
To Find:
(a) Current = I = ?
(b) Phase angle = ф = ?
(c) Power factor = cos ф = ?
(d) Power consumed =<P>= ?
Solution:
(a) Current = I = ?
The current is given by:
IrmsIrms = VrmsZVrmsZ ---------(1)
But the impedance Z is unknown So
Z = √R2+X2L√R2+X2L -----------(2)
Also, we will find the value of XLXL
XLXL = ယ L = 2ㄫf L
by putting values
XLXL = 2 x 3.1416 x 50 Hz x 31.8x10⁻³ H
XLXL = 9.985 Ω
Now eqn(2)
Z = √(7Ω)2+(9.985Ω)2√(7Ω)2+(9.985Ω)2
Z = √49Ω2+99.704Ω2√49Ω2+99.704Ω2
Z = √148.704Ω2√148.704Ω2
Z = 12.194 Ω
Thus equation (1) will be
Irms = 230V12.194Ω
Irms = 18.86 A -----------------------Ans. (1)
(b) Phase angle = ф = ?
Phase angle can be calculated as
ф = tan⁻¹(XLR)
ф = tan⁻¹(9.985Ω7Ω)
ф = tan⁻¹(1.426)
ф = 55° ---------------------Ans. (2)
(c) Power factor = cos ф = ?
cos ф = cos 55° = 0.573 ---------------Ans. (3)
(d) Power consumed = <P> = ?
<P> = IrmsVrms cos ф
<P> = 18.86 A x230 V x 0.573
<P> = 2485.559 w -----------------Ans. (4)
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