1
GATE EE 2007
+2
-0.6
A three phase balanced star connected voltage source with frequency $$\omega \,\,rad/s$$ is connected to a star connected balanced load which is purely inductive. The instantaneous line currents and phase to neutral voltages are denoted by $$\left( {{i_a},{i_b},{i_c}} \right)$$ and $$\left( {{V_{an}},\,\,{V_{bn}},\,\,{V_{cn}}} \right)$$ respectively and their $$rms$$ values are denoted by $$V$$ and $$1.$$ If $$R = \left[ {{V_{an}}\,\,{V_{bn}}\,\,{V_{cn}}} \right]\left[ {\matrix{ 0 & {{1 \over {\sqrt 3 }}} & { - {1 \over {\sqrt 3 }}} \cr { - {1 \over {\sqrt 3 }}} & 0 & {{1 \over {\sqrt 3 }}} \cr {{1 \over {\sqrt 3 }}} & { - {1 \over {\sqrt 3 }}} & 0 \cr } } \right]\left[ {\matrix{ {{i_a}} \cr {{i_b}} \cr {{i_c}} \cr } } \right],$$\$
then the magnitude of $$R$$ is
A
$$3$$ $$V{\rm I}$$
B
$$V{\rm I}$$
C
$$0.7$$ $$V{\rm I}$$
D
$$0$$
2
GATE EE 2006
+2
-0.6
A $$400V$$, $$50$$ $$Hz,$$ three phase balanced source supplies power to a star connected load whose rating is $$12\,\,\angle 3\,\,kVA,$$ $$0.8$$ $$pf$$ (lag). The rating $$($$in $$kVAR)$$ of the delta connected (capacitive) reactive power bank necessary to bring the $$pf$$ to unity is
A
$$28.78$$
B
$$21.60$$
C
$$16.60$$
D
$$12.47$$
3
GATE EE 2003
+2
-0.6
A balanced delta connected load of $$\left( {8 + j6} \right)$$ $$\Omega$$ per phase is connected to a $$400V,$$ $$50Hz,$$ $$3-$$ phase supply lines. If the input power factor is to be improved to $$0.9$$ by connecting a bank of star connected capacitors, the required $$kV$$ $$AR$$ of the bank is
A
$$42.7$$
B
$$10.2$$
C
$$28.8$$
D
$$38.4$$
4
GATE EE 1994
Numerical
+2
-0
A set of $$3$$ equal resistors, each of value $${R_X},$$ connected in star across $$RYB$$ of given Fig. consumes the same power as the unbalanced delta-connected load shown. The value of $${R_X}$$ is _____________ $$\Omega .$$