# AC theory (2 motors in parallel)

b. The phase angle

c. The total impedance (i.e. the impedance as seen by the electrical supply)

d. The power factor

Answers

For the phase diagram please see attached figure.

$I = sqrt{[(U/R1+U/R2)^2 + (U/XL-U/X c)^2]} =$

$= 230*sqrt{(1/6+1/8)^2 +(1/8 -1/15)^2} =$

$=230*sqrt(0.085+0.0034)=68.385 A$

$tan(phi) = (1/XL-1/X C)/(1/R1+1/R2) = (1/8-1/15)/(1/6+1/8) =0.0583/0.2916=0.2$

$phi =11.31 degree$

$I = U/Z$

$Z = U/I = 230/68.385 =3.363 ohm$

another way to compute Z is

$1/Z = sqrt{[(1/R1 +1/R2)^2 + (X C parallel XL)^2]} =$

$= sqrt{[(R1+R2/R1*R2)^2 + (X C-XL)/(X C*XL))^2]} =$

$= sqrt{[(6+8)/(6*8))^2 +(15-8/(15*8))^2]} =$

$= sqrt{(0.085 +0.0034)}=0.297$

$Z =1/0.297 =3.363 ohm$

Power factor $= P/Pa$

$Pa = U*I = 230*68.385 =15728.55 W$

$P = U^2/R eq = 230*230/3.428 =15431.74$

$R eq = R1*R2/(R1+R2) = 6*8/(6+8) =3.428$

Power factor $= 15431.74/15728.55 =0.9811 =98.11%$