Electrical Engineering - Three-Phase Systems in Power Applications - Discussion

Correct answer is D:

as Va and Vb are 90 degree apart so;

Va=120<0; ---> polar form
Vb=120<90 ---> polar form.

Lets convert it into rectangular form
Va=120*(cos(0)+jsin(0)).
Va=120;
Vb=120*(cos(90)+jsin(90)).
Vb=j120;.

Now calculating current;
Ia= 120/90;
Ia=1.33;
Ib= j120/90;
Ib=j1.33;.

Total Current=Ia+Ib.
I=1.33+j1.33;
Converting back to polar form.
magnitude=
I= √((1.33)^2+(j1.33)^2).
I=1.76;.
θ=tan inv(1.33/1.33);.
θ=45.

So;
I=1.76<45;
Thanks; Hope it works

There are two loads, hence the current passes through both the resistors and common Neutral

V= 120V each phase
1/R= 1/90+1/90=2/90= 1/45
R=45Ω

V = IR.
I = V/R.

Hence neutral Current
I=V/R1+V/R2
=(120/90)+(120/90).

I = 1.33+1.33 = 2.66 amp.
Or I = 120/45= 2.66 Amp.

Whereas Generator is two-phase so the Neutral Current is
IN = I * (difference in Phase angle/Total +ve angle)
the difference in phase=120.

Total angle start from zero then high and zero=180
= 2.66 * (120/180).

Given 3 phase currents; A, B, and C, we say that neutral current is equal to (A^2 + B^2 + C^2)-(AB + BC + CA).

Therefore, given 2 phase currents, A and B, netrual current is equal to (A^2 + B^2)-(AB)
Ip=Vp/Rp ==>> 120/90 = 1.3333A.

Since A=B, then neutral current is equal to (A^4)-(A^2) = A^2.
1.3333^2 = 1.7777.

It is simple question since, two phase generator is connected to two load resistor therefore resistance = 90 * 90 = 8100 & total voltage = 120 * 120 = 14400.

Therefore required current through common neutral line is = 14400/8100 = 1.77A.

There is the two phase.

120*120 = 14400 volt.

90*90 = 8100 ohm.

Hence current (i) = v/r.

= 14400/8100 = 1.77 amp.

Give me the correct explanation!

V = IR.
Total resistance of two resistors(is parallel) is:

45ohms,
Voltage is 120v,
Current is =120/45,
Current is 2.66 amps.

Parallel connection, voltage same v = 120 v, R = 45 v, I = 120/45 = 2.66 A.

@Amjad.

How have you done this. Is there any formula like that?

I am correcting answer of @Mr Rasood.

I = 120/90*1.414 = 1.88 A since the currents are 90 degrees out of phase.

Could also be written as I = 1.33 + j 1.33 (rectangular form) = 1.88 A at 45 degrees (polar form).

= 1.88*cos 45.

= 1.88*1/square root (2).

= 1.88/1.41 = 1.33.