Question

Two balanced Y-connected loads, one drawing 10 kW at 0.8 power factor lagging and the other 15 kW at 0.9 power factor leading, are connected in parallel and supplied by a balanced three-phase Y-connected, 480-V source.
(a) Determine the source current.
(b) If the load neutrals are connected to the source neutral by a zero-ohm neutral wire through an ammeter, what will the ammeter read?

Answer 1

Answer:

a.  30.O7A

b.  no reading

Explanation:

for the first load with power factor 0.8, we calculate the reactive power

note the reactive power is calculated as

$Q=Ptan(cos^{-1}\alpha )$

where p=power

a. for the first load the reactive power is

$Q=10tan(cos^{-1} 0.8)\\Q=7.5kvar$

for the second load the reactive power is

$Q=-15tan(cos^{-1} 0.9)\\Q=-7.265kvar$

The total reactive power is the summation of both reactive power in he load

$Q_{total}=7.5+(-7.265)\\Q=-0.235kvar$

and the total real power is 25kw

Hence using Pythagoras theorem to calculate the apparent power we have

$S=\sqrt{P^{2}+Q^{2}}\\ S=25.001KVA$  

Hence we can determine the source current using

$S=\sqrt{3}VI\\ I=\frac{25.001*10^{3}}{\sqrt{3} *480} \\I=30.07A$

b. in a balance 3phase system, there is no neutral current, Hence the ammeter will read zero current