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

The circuit will be balanced due to the same amount of load on both phases and so the current through the neutral wire must be zero.

The 2 resistors are connected in parallel or series, the result (I) may vary accordingly.

The right answer is option *C*
120/90 = 4/3.
4/3+1.3 = 2.63.

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.

Phase difference = (360°/number of phases). Therefore we have 180° phase difference in a 2 phase system. Since the load is resistive and balanced. The load currents will also have 180° phase difference.

Therefore the current in neutral which is phasor sum of load currents is also zero.

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

For 2ac, both phases will be 90° apart. thus for 'i' instantaneous current, there will be -I current, means I current in opposite direction.

Thus resultant current will be zero.

Since it is AC we should take RMS voltage into consideration. The RMS voltage = (Peak Voltage/SquareRoot(120)).

Hence the current=(2*(squareRoot(120)))/90==1.88.

Give me the correct explanation!